We propose a fully conservative high-order upwind multi-moment method for the conservation equation. The proposed method is based on a third-order polynomial interpolation function and semi-Lagrangian formulation, and is a variant of the CIP-CSL3 (constrained interpolation profile conservative semi-Lagrangian scheme with third-order polynomial function) method. The third-order interpolation function is constructed based on three constraints in the upwind cell (two boundary values and a cell average) and a constraint in the downwind cell (a cell center value). The proposed method shows 4th-order accuracy in a benchmark problem (sine wave propagation). We also propose a less oscillatory formulation of the proposed method. The less oscillatory formulation can minimize numerical oscillations. These methods were validated through scalar transport problems, and compressible flow problems (shock tube and 2D explosion problems). This article is protected by copyright. All rights reserved.

In this paper pressure stability through the suppression of high frequency pressure oscillations in the Moving Particle Semi-implicit (MPS) method is presented. To obtain a stable pressure field we improve the free surface particle search algorithm. Pressure stability follows from the suppression of high frequency pressure oscillations due to a correction in the Laplacian operator of the Poisson pressure equation and from the correction of the pressure gradient operator. The three proposed modifications are applied gradually and compared with the MPS method to show the improvements in the hydrostatic pressure and dam breaking problems. To validate the suppression of the high frequency numerical pressure oscillations, the modified Moving Particle Semi-implicit (mMPS) method with and without a removable wall are compared with published dam breaking experiment pressure measurements. This article is protected by copyright. All rights reserved.

Numerical modeling of multiphase flow generally requires a special procedure at the solid wall in order to be consistent with Young's law for static contact angles. The standard approach in the lattice Boltzmann method, which consists of imposing fictive densities at the solid lattice sites, is shown to be deficient for this task. Indeed, fictive mass transfer along the boundary could happen and potentially spoil the numerical results. In particular, when the contact angle is less than 90 degrees, the deficiencies of the standard model are major. Various videos that demonstrate this behaviour are provided (Appendix A). A new approach is proposed and consists of directly imposing the contact angle at the boundaries in much the same way as Dirichlet boundary conditions are generally imposed. The proposed method is able to retrieve analytical solutions for static contact angles in the case of straight and curved boundaries even when variable density and viscosity ratios between the phases are considered. Although the proposed wetting boundary condition is shown to significantly improve the numerical results for one particular class of lattice Boltzmann model, it is believed that other lattice Boltzmann multiphase schemes could also benefit from the underlying ideas of the proposed method. The proposed algorithm is two-dimensional and the D2Q9 lattice is used. This article is protected by copyright. All rights reserved.

In this paper we show how the spectral formulation of Baker, Meiron and Orszag can be used to solve for waves on water of infinite depth confined between two flat, vertical walls, and also how it can be modified to take into account water of finite depth with a spatially-varying bottom. In each case, we use Chebyshev polynomials as the basis of our representation of the solution and filtering to remove spurious high-frequency modes. We show that spectral accuracy can be achieved until wave breaking, plunging or wall impingment occurs in two model problems. This article is protected by copyright. All rights reserved.

In this paper the thermal load on an actively cooled lobed strut injector for scramjet (supersonic combustion ramjet) applications is investigated numerically. This requires coupled simulations of the strut internal and external flow fields together with the heat conduction in the solid injector body. In order to achieve a fast mixing, the lobed strut is positioned at the channel axis to inject hydrogen into the core of a Mach 3 air stream. There it is exposed to the extremely high temperatures of the high speed flow. While the external air and hydrogen flows are supersonic the strut internal hydrogen flow is mainly subsonic, in some regions at very low Mach numbers. To enable a simulation of the internal flow field which ranges from very low to very high Mach numbers (approximately Mach 2.25 at the nozzle exit), a preconditioning technique is employed. The compressible finite-volume scheme uses a spatially fourth order MLP (multi-dimensional limiting process) [1, 2] discretization which is used here for a first time to simulate a geometrically and fluid mechanically highly complex problem. It will be demonstrated that besides its high accuracy the MLP scheme is numerically stable even in case of demanding practical applications. The coupled simulation of the lobed strut injector delivers unique insight into the flow phenomena inside and outside the strut, the heat fluxes, the temperature distribution in the solid material, the required hydrogen mass flux with respect to cooling requirements and details concerning the conditions at the exit of the injector. This article is protected by copyright. All rights reserved.

In this paper, we introduce a shock capturing artificial viscosity technique for high-order unstructured mesh methods. This artificial viscosity model is based on a non-dimensional form of the divergence of the velocity. The technique is an extension and improvement of the dilation-based artificial viscosity methods introduced in Premasuthan, Liang and Jameson [Computers & Fluids, 98:122-133] and further extended in Nguyen and Peraire [Proceedings of the 20th AIAA Computational Fluid Dynamics Conference, AIAA paper 2011-3060]. The approach presented has a number attractive properties including non-dimensional analytical form, sub-cell resolution, and robustness for complex shock flows on anisotropic meshes. We present extensive numerical results to demonstrate the performance of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.

An advanced hybrid lumped parameter code for the simulation of Pulsating Heat Pipes is developed. Being able to simulate transient operative conditions and removing common physical simplified assumptions, it represents a step forward with respect to the present models of passive two-phase systems. Mass, momentum and energy balances account for the thermal and fluid-dynamics phenomena. Heterogeneous and homogeneous phase changes are directly integrated. In addition, a fitting correlation for the wall/vapor heat transfer coefficient is implemented and tuned against experimental data in order to evaluate the influence of the liquid film on conjugate heat transfer. The resulting numerical tool have been validated against experimental data achieved testing a copper Pulsating Heat Pipe during the 58^{th} ESA Parabolic Flight Campaign in several operative conditions and transient gravity levels. The predicted results show very good matching with the actual thermo-physical behavior of the system.

The approximation of reduced linear evolution operator (propagator) via Dynamic Mode Decomposition is addressed for both linear and nonlinear events. The 2D unsteady supersonic underexpanded jet, impinging the flat plate in nonlinear oscillating mode, is used as the first test problem for both modes. Large memory savings for the propagator approximation are demonstrated. Corresponding prospects for the estimation of receptivity and singular vectors are discussed. The shallow water equations are used as the second large scale test problem. Excellent results are obtained for the proposed optimized DMD method of the shallow water equations when compared with recent POD/DEIM based model reduction results in the literature. This article is protected by copyright. All rights reserved.

A hybrid particle-mesh method was developed for efficient and accurate simulations of two-phase flows. In this method, the main component of the flow is solved using the CIP/MM FVM; the two-phase interface is rendered using the finite volume particle (FVP) method. The effect of surface tension is evaluated using the continuum surface force model. Numerical particles in the FVP method are distributed only on the surface of the liquid in simulating the interface between liquid and gas; these particles are used to determine the density of each mesh grid. An artificial term was also introduced to mitigate particle clustering in the direction of maximum compression and sparse discretization errors in the stretched direction. This enables accurate interface tracking without diminishing numerical efficiency. Two benchmark simulations are used to demonstrate the validity of the method developed as well as its numerical stability.

This paper presents a stabilized XFEM-based fluid formulation to embed arbitrary fluid patches into a fixed background fluid mesh. The new approach is highly beneficial when it comes to computational grid generation for complex domains, as it allows locally increased resolutions independent from size and structure of the background mesh. Motivating applications for such a domain decomposition technique are complex fluid-structure interaction problems, where an additional boundary layer mesh is used to accurately capture the flow around the structure. The objective of this work is to provide an accurate and robust XFEM-based coupling for low- as well as high-Reynolds-number flows. Our formulation is built from the following essential ingredients: Coupling conditions on the embedded interface are imposed weakly using Nitsche's method supported by extra terms to guarantee mass conservation and to control the convective mass transport across the interface for transient viscous- and convection-dominated flows. Residual-based fluid stabilizations in the interior of the fluid subdomains and accompanying face-oriented fluid and ghost-penalty stabilizations in the interface zone stabilize the formulation in the entire fluid domain. A detailed numerical study of our stabilized embedded fluid formulation, including an investigation of variants of Nitsche's method for viscous flows, shows optimal error convergence for viscous- and convection-dominated flow problems independent of the interface position. Challenging two- and three-dimensional numerical examples highlight the robustness of our approach in all flow regimes: benchmark computations for laminar flow around a cylinder, a turbulent driven cavity flow at Re = 10000 and the flow interacting with a 3D flexible wall. This article is protected by copyright. All rights reserved.

An improved high-order accurate WENO finite volume method based on unstructured grids for compressible multi-fluids flow is proposed in this paper. The third order accuracy WENO finite volume method based on triangle cell is used to discrete the governing equations. To have higher order of accuracy, the P1 polynomial is reconstructed firstly. After that, the P2 polynomial is reconstructed from the combination of the P1. The reconstructed coefficients are calculated by analytical form of inverse matrix rather than the numerical inversion. This greatly improved the efficiency and the robustness. Four examples are presented to examine this algorithm. Numerical results show that there is no spurious oscillation of velocity and pressure across the interface and high-order accurate result can be achieved. This article is protected by copyright. All rights reserved.

In this paper, a local mesh refinement (LMR) scheme on Cartesian grids for large-eddy simulations is presented. The approach improves the calculation of ghost cell pressures and velocities and combines LMR with high-order interpolation schemes at the LMR interface and throughout the rest of the computational domain to ensure smooth and accurate transition of variables between grids of different resolution. The approach is validated for turbulent channel flow and flow over a matrix of wall-mounted cubes for which reliable numerical and experimental data are available. Comparisons of predicted first-order and second-order turbulence statistics with the validation data demonstrated a convincing agreement. Importantly, it is shown that mean streamwise velocities and fluctuating turbulence quantities transition smoothly across coarse-to-fine and fine-to-coarse interfaces. Copyright © 2016 John Wiley & Sons, Ltd.

This paper introduces and validates a local mesh refinement approach for simulations of turbulent flows in complex domains. The method features high-order interpolation schemes at the fine-coarse mesh interfaces and uses up to fourth-order central differencing schemes for convective and diffusive fluxes. It is shown that the local mesh refinement method is able to predict accurately first-order and second-order statistics of two challenging flows, a turbulent channel flow and the flow over a matrix of cubes. The method offers significant savings of computational resources due to the placement of very fine meshes into critical areas, for instance around the cubes, while for the rest of the domain, coarser meshes are employed.

Discontinuous Galerkin (DG) methods allow high-order flow solutions on unstructured or locally refined meshes by increasing the polynomial degree and using curved instead of straight-sided elements. However, one of the currently largest obstacles to applying these methods to aerodynamic configurations of medium to high complexity is the availability of appropriate higher-order curved meshes.

In this article, we describe a complete chain of higher-order unstructured grid generation and higher-order DG flow solution applied to a turbulent flow around a three-dimensional high-lift configuration. This includes (i) the generation of an appropriately coarse straight-sided mesh; (ii) the evaluation of additional points on the computer-aided design geometry of the curved-wall boundary for defining a piecewise polynomial boundary representation; (iii) a higher order mesh deformation to translate the curvature from the wall boundary into the interior of the computational domain; and (iv) the description of a DG discretization, which is sufficiently stable to allow a flow computation on the resulting curved mesh. Finally, a fourth-order flow solution of the Reynolds-averaged Navier–Stokes and *k*-*ω* turbulence model equations is computed on a fourth-order unstructured hybrid mesh around the three-dimensional high-lift simulation of wing-flow noise generation configuration. Copyright © 2016 John Wiley & Sons, Ltd.

This paper includes a description of a complete chain of unstructured curvilinear grid generation and higher order Discontinuous Galerkin flow solution applied to a turbulent flow around a 3D high-lift configuration. A fourth order flow solution of the RANS and k-w turbulence model equations is computed on a fourth order unstructured hybrid (mixed-element) mesh around the 3D high-lift SWING configuration. A highly resolved flow solution is obtained featuring a complex vortex system.

We investigate implicit large eddy simulation of the Taylor–Green vortex, Comte-Bellot–Corrsin experiment, turbulent channel flow and transitional and turbulent flow over an SD7003 airfoil using the high-order unstructured correction procedure via reconstruction (CPR) scheme, also known as the flux reconstruction scheme. We employ P1 (second-order) to P5 (sixth-order) spatial discretizations. Results show that the CPR scheme can accurately predict turbulent flows without the addition of a sub-grid scale model. Numerical dissipation, concentrated at the smallest resolved scales, is found to filter high-frequency content from the solution. In addition, the high-order schemes are found to be more accurate than the low-order schemes on a per degree of freedom basis for the canonical test cases we consider. These results motivate the further investigation and use of the CPR scheme for simulating turbulent flows. Copyright © 2016 John Wiley & Sons, Ltd.

We perform simulations of turbulent flows using the correction procedure via reconstruction (CPR) scheme. Our results demonstrate that the CPR scheme can be used for implicit large eddy simulation, without the addition of an explicit sub-grid scale model. We find that the high-order schemes are generally more accurate than the low-order schemes on a per degree of freedom basis.

Accurately characterizing the forces acting on particles in fluids is of fundamental importance for understanding particle dynamics and binding kinetics. Conventional asymptotic solutions may lead to poor accuracy for neighboring particles. In this paper, we develop an accurate boundary integral method to calculate forces exerted on particles for a given velocity field. We focus our study on the fundamental two-bead oscillating problem in an axisymmetric frame. The idea is to exploit a correspondence principle between the unsteady Stokes and linear viscoelasticity in the Fourier domain such that a unifying boundary integral formulation can be established for the resulting Brinkman equation. In addition to the dimension reduction vested in a boundary integral method, our formulation only requires the evaluation of single-layer integrals, which can be carried out efficiently and accurately by a hybrid numerical integration scheme based on kernel decompositions. Comparison with known analytic solutions and existing asymptotic solutions confirms the uniform third-order accuracy in space of our numerical scheme. Copyright © 2016 John Wiley & Sons, Ltd.

We develop an accurate boundary integral method to calculate forces exerted on particles in unsteady Stokes flow and linear viscoelastic fluids. Our numerical method is third-order accurate uniformly in space and corrects the error due to the poles at the axis of symmetry.

The influence of mesh motion on the quality of large eddy simulation (LES) was studied in the present article. A three-dimensional, turbulent pipe flow (*R**e*_{τ}=360) was considered as a test case. Simulations with both stretching and static meshes were carried out in order to understand how mesh motion affects the turbulence statistics. The spatial filtering of static and moving mesh direct numerical simulation (DNS) data showed how an ideal LES would perform, while the comparison of DNS cases with static and moving meshes revealed that no significant numerical errors arise from the mesh motion when the simulation is fully resolved. The comparison of the filtered fields of the DNS with a moving mesh with the corresponding LES fields revealed different responses to mesh motion from different numerical approaches. A straightforward test was applied in order to verify that the moving mesh works consistently in LES: when the mesh is stretched in the streamwise direction, the moving mesh results should be in between the two extremal resolutions between which the mesh is stretched. Numerical investigations using four different LES approaches were carried out. In addition to the Smagorinsky model, three implicit LES approaches were used: linear interpolation (non-dissipative), the Gamma limiter (dissipative), and the scale-selective discretisation (slightly dissipative). The results indicate that while the Smagorinsky and the scale-selective discretisation approaches produce results consistent with the resolution of the non-static mesh, the implicit LES with linear interpolation or the Gamma scheme do not. Copyright © 2016 John Wiley & Sons, Ltd.

The effect of mesh motion on the outcome of a large eddy simulation was studied in the present article. A turbulent pipe flow (*Re _{t}* = 360) was used as a test case. The results of this study indicate that runtime mesh deformation can have a noticeable effect on the velocity and energy statistics of a large eddy simulation.

Particle-based CFD methods are powerful approaches to investigate free surface, multiphase flows, and fluid structure interaction problems because of their ability of tracking moving fluid interface even with huge deformations or fragmentation and merging. However, many fluid interface particle detection techniques are simple to implement but with low accuracy or provide relatively good detection results at complicated implementation cost or higher computational time. In case of incompressible flow simulation methods solving the Poisson equation of pressure, such as the moving particle semi-implicit method, boundary particles detection techniques' accuracy affects precision and stability of pressure computation and interaction between fluid phases. In the present work, a new fluid interface particle detection technique is proposed to improve the accuracy of the boundary particles detection and keep the implementation easy. Denominated as the neighborhood particles centroid deviation technique, it is a two-criteria technique based on the particle number density and the neighborhood particles weighted geometric center deviation. Compared with other techniques, the proposed neighborhood particles centroid deviation technique shows the best results by eliminating false interface particles inside the fluid domain and keeping the interface particles layer thin and regular. As a result, relatively stable pressure time histories and more consistent pressure and velocity fields are achieved. Copyright © 2016 John Wiley & Sons, Ltd.

Particle-based CFD methods are powerful approaches to investigate fluid flows with huge deformations or fragmentation and merging because of their ability of tracking moving interfaces. However, many fluid interface particle detection techniques are simple to implement but with low accuracy or provide relatively good detection results at complicated implementation or higher computational time. Besides a review of the main available techniques, in this paper, a new technique is proposed to improve the accuracy while keeping implementation easy and with low computational cost.

Large-eddy simulation (LES) consists in explicitly simulating the large scales of the fluid motion and in modeling the influence of the smallest scales. Thanks to the steady growth of computational resources, LES can now be used to simulate realistic systems with complex geometries. However, when LES is used in such complex geometries, an adequate mesh has to be determined to perform valid LES. In this work, a strategy is proposed to assess the quality of a given mesh and to adapt it locally. Two different criteria are used as mesh adaptation criteria. The first criterion is defined to ensure a correct discretization of the mean field, whereas the second criterion is defined to ensure enough explicit resolution of turbulent scales motions. The use of both criteria is shown in canonical flow cases. As a second part of this work, a numerical strategy for mesh adaptation in high-performance computing context is proposed by coupling the flow solver, YALES2, and the remeshing library, MMG3D, for massively parallel computations. This coupling enables an efficient and parallel remeshing of grids alleviating any memory or performance issues encountered in sequential tools. This strategy is finally applied to the simulation of the isothermal flow in a complex meso-combustor to demonstrate the applicability of the adaptation methodology to complex turbulent flows. Copyright © 2015 John Wiley & Sons, Ltd.

This paper presents a novel mesh adaptation strategy in the context of Large Eddy Simulation (LES). Two mesh quality criteria are defined, one for the discretization of the mean field and the other for the turbulent kinetic energy resolution. A parallel mesh adaptation strategy, based on these criteria, is proposed and applied to the simulation of the turbulent iso-thermal flow in a complex meso-scale combustor. It shows a large improvement in the quality of the results with a moderate over-cost.

We have investigated a collocation methodology for the numerical simulation of Fujiwhara interactions between cyclone scale vortices. The method is validated by computing the rotational period (t*) of the Fujiwhara interaction, as well as by simulating concentric eyewal patterns and barotropic instability of tropical cyclones. Numerical simulation Fujiwhara interactions at moderately high Reynolds numbers, such as for , show that the kinetic energy of cyclones is consolidated into larger scales with a concurrent enstrophy cascade.

A three-dimensional numerical model is presented for the simulation of unsteady non-hydrostatic shallow water flows on unstructured grids using the finite volume method. The free surface variations are modeled by a characteristics-based scheme, which simulates sub-critical and super-critical flows. Three-dimensional velocity components are considered in a collocated arrangement with a *σ*-coordinate system. A special treatment of the pressure term is developed to avoid the water surface oscillations. Convective and diffusive terms are approximated explicitly, and an implicit discretization is used for the pressure term to ensure exact mass conservation. The unstructured grid in the horizontal direction and the *σ* coordinate in the vertical direction facilitate the use of the model in complicated geometries. Solution of the non-hydrostatic equations enables the model to simulate short-period waves and vertically circulating flows. Copyright © 2015 John Wiley & Sons, Ltd.

A numerical model was presented for the simulation of three-dimensional unsteady non-hydrostatic shallow water flows. A sigma coordinate system with a collocated arrangement of three-dimensional velocity components was used to simulate the variation of water depth during the time steps. The numerical results showed that the model is capable of producing non-oscillatory and accurate results.

In this paper, we propose new energy dissipative characteristic numerical methods for the approximation of diffusive Oldroyd-B equations that are based either on the finite element or finite difference discretization. We prove energy stability of both schemes and illustrate their behavior on a series of numerical experiments. Using both the diffusive model and the logarithmic transformation of the elastic stress, we are able to obtain methods that converge as mesh parameter is refined. Copyright © 2015 John Wiley & Sons, Ltd.

We propose new energy dissipative characteristic schemes for the diffusive Oldroyd-B equations, which are based either on the finite element or finite difference discretization. Using both the diffusive model and the logarithmic transformation of the elastic stress, we are able to obtain methods that converge as mesh parameter is refined.

Central moment lattice Boltzmann method (LBM) is one of the more recent developments among the lattice kinetic schemes for computational fluid dynamics. A key element in this approach is the use of central moments to specify the collision process and forcing, and thereby naturally maintaining Galilean invariance, an important characteristic of fluid flows. When the different central moments are relaxed at different rates like in a standard multiple relaxation time (MRT) formulation based on raw moments, it is endowed with a number of desirable physical and numerical features. Because the collision operator exhibits a cascaded structure, this approach is also known as the cascaded LBM. While the cascaded LBM has been developed sometime ago, a systematic study of its numerical properties, such as the accuracy, grid convergence, and stability for well-defined canonical problems is lacking, and the present work is intended to fulfill this need. We perform a quantitative study of the performance of the cascaded LBM for a set of benchmark problems of differing complexity, viz., Poiseuille flow, decaying Taylor–Green vortex flow, and lid-driven cavity flow. We first establish its grid convergence and demonstrate second-order accuracy under diffusive scaling for both the velocity field and its derivatives, that is, the components of the strain rate tensor, as well. The method is shown to quantitatively reproduce steady/unsteady analytical solutions or other numerical results with excellent accuracy. The cascaded MRT LBM based on the central moments is found to be of similar accuracy when compared with the standard MRT LBM based on the raw moments, when a detailed comparison of the flow fields are made, with both reproducing even the small scale vortical features well. Numerical experiments further demonstrate that the central moment MRT LBM results in significant stability improvements when compared with certain existing collision models at moderate additional computational cost. Copyright © 2015 John Wiley & Sons, Ltd.

A comparative numerical study of the cascaded MRT LBM, which is based on central moments, and the standard MRT LBM, which is based on raw moments, is presented. For example, this figure shows that the streamlines in the cavity flow for Re = 5000 computed using the cascaded LBM is in excellent agreement with those of the standard MRT LBM. Furthermore, substantial improvement in the numerical stability is also achieved with the cascaded LBM.

We present a parameter-free stable maximum-entropy method for incompressible Stokes flow. Derived from a least-biased optimization inspired by information theory, the meshfree maximum-entropy method appears as an interesting alternative to classical approximation schemes like the finite element method. Especially compared with other meshfree methods, e.g. the moving least-squares method, it allows for a straightforward imposition of boundary conditions. However, no Eulerian approach has yet been presented for real incompressible flow, encountering the convective and pressure instabilities. In this paper, we exclusively address the pressure instabilities caused by the mixed velocity-pressure formulation of incompressible Stokes flow. In a preparatory discussion, existing stable and stabilized methods are investigated and evaluated. This is used to develop different approaches towards a stable maximum-entropy formulation. We show results for two analytical tests, including a presentation of the convergence behavior. As a typical benchmark problem, results are also shown for the leaky lid-driven cavity. The already presented information-flux method for convection-dominated problems in mind, we see this as the last step towards a maximum-entropy method capable of simulating full incompressible flow problems. Copyright © 2015 John Wiley & Sons, Ltd.

We present a parameter-free stable maximum-entropy method for incompressible Stokes flow. Stable and stabilized velocity-pressure formulation that already exist for other computational methods are investigated and evaluated in order to develop different approaches towards a stable maximumentropy scheme. The method's excellent performance is shown by results for two analytical tests, including a presentation of the convergence behavior, and for the leaky lid-driven cavity as a typical benchmark problem.

In this paper, we propose for the first time a linearly coupled, energy stable scheme for the Navier–Stokes–Cahn–Hilliard system with generalized Navier boundary condition. We rigorously prove the unconditional energy stability for the proposed time discretization as well as for a fully discrete finite element scheme. Using numerical tests, we verify the accuracy, confirm the decreasing property of the discrete energy, and demonstrate the effectiveness of our method through numerical simulations in both 2-D and 3-D. Copyright © 2015 John Wiley & Sons, Ltd.

In the study of the phase-field model for the moving contact line problem, a linear and energy stable numerical scheme was proposed in the paper for solving the Navier-Stokes-Cahn-Hilliard system subject to a new set of complex boundary conditions. Performance and visualization were provided in the work.

A hybrid time stepping scheme is developed and implemented by a combination of explicit Runge–Kutta with implicit LU-SGS scheme at the level of system matrix. In this method, the explicit scheme is applied to those grid cells of blocks that have large local time steps; meanwhile, the implicit scheme is applied to other grid cells of blocks that have smaller allowable local time steps in the same flow field. As a result, the discretized governing equations can be expressed as a compound of explicit and implicit matrix operator. The proposed method has been used to compute the steady transonic turbulent flow over the RAE 2822 airfoil. The numerical results are found to be in excellent agreement with the experimental data. In the validation case, the present scheme saved at least 50% of the memory resources compared with the fully implicit LU-SGS. Copyright © 2015 John Wiley & Sons, Ltd.

We proposed a combination of explicit Runge–Kutta with implicit LU-SGS scheme at the level of system matrix. The combination makes the discretized governing equations expressed as a compound of explicit and implicit matrix operator. Numerical results show that the convergence rate of the present scheme is almost the same as that of the LU-SGS implicit scheme for the same splitting grid and the same CFL number. In the numerical case, the present scheme saved 50% of the memory resources compared with the fully implicit LU-SGS.

In this paper, we propose an interfacial pressure correction algorithm for smoothed particle hydrodynamics (SPH) simulation of multiphase flows with large density ratios. This correction term is based on the assumption of small deformation of the interface, and derived from perturbation expansion analysis. It is also proven to be applicable in cases with complex interfaces. This correction algorithm helps to overcome the discontinuities of the pressure gradient over the interfaces, which may cause unphysical gap between different phases. This proposed correction algorithm is implemented on a recent multiphase SPH model, which is based on the assumption of pressure continuity over the interfaces. The coupled dynamic solid boundary treatment is used to simulate solid walls; and a cut-off pressure is applied to avoid negative particle pressure, which may cause computational instabilities in SPH. Three numerical examples of air–water flows, including sloshing, dam breaking, and water entry, are presented and compared with experimental data, indicating the robustness of our pressure correction algorithm in multiphase simulations with large density ratios. Copyright © 2015 John Wiley & Sons, Ltd.

In this work, we propose an interfacial pressure correction algorithm for SPH simulation of multiphase flows with large density ratios. This correction algorithm helps to improve the stability of the original model, especially for long-time problems.

A discontinuous Galerkin nonhydrostatic atmospheric model is used for two-dimensional and three-dimensional simulations. There is a wide range of timescales to be dealt with. To do so, two different implicit/explicit time discretizations are implemented. A stabilization, based upon a reduced-order discretization of the gravity term, is introduced to ensure the balance between pressure and gravity effects. While not affecting significantly the convergence properties of the scheme, this approach allows the simulation of anisotropic flows without generating spurious oscillations, as it happens for a classical discontinuous Galerkin discretization. This approach is shown to be less diffusive than usual spatial filters. A stability analysis demonstrates that the use of this modified scheme discards the instability associated with the usual discretization. Validation against analytical solutions is performed, confirming the good convergence and stability properties of the scheme. Numerical results demonstrate the attractivity of the discontinuous Galerkin method with implicit/explicit time integration for large-scale atmospheric flows. Copyright © 2015 John Wiley & Sons, Ltd.

A stabilization, based upon a reduced-order discretization of the gravity term, ensures the balance between pressure and gravity effects. Validation with a stability analysis and numerical experiments confirming the correct convergence rate.

We consider a Leray model with a deconvolution-based indicator function for the simulation of incompressible fluid flow at moderately large Reynolds number (in the range of a few thousands) with under-resolved meshes. For the implementation of the model, we adopt a three-step algorithm called *evolve–filter–relax* that requires (i) the solution of a Navier–Stokes problem, (ii) the solution of a Stokes-like problem to filter the Navier–Stokes velocity field, and (iii) a final relaxation step. We take advantage of a reformulation of the evolve–filter–relax algorithm as an operator-splitting method to analyze the impact of the filter on the final solution versus a direct simulation of the Navier–Stokes equations.

In addition, we provide some direction for tuning the parameters involved in the model based on physical and numerical arguments. Our approach is validated against experimental data for fluid flow in an idealized medical device (consisting of a conical convergent, a narrow throat, and a sudden expansion, as recommended by the U.S. Food and Drug Administration). Numerical results are in good quantitative agreement with the measured axial components of the velocity and pressures for two different flow rates corresponding to turbulent regimes, even for meshes with a mesh size more than 40 times larger than the smallest turbulent scale. After several numerical experiments, we perform a preliminary sensitivity analysis of the computed solution to the parameters involved in the model. Copyright © 2015 John Wiley & Sons, Ltd.

We adopt a Leray model for the simulation of fluid flows at moderately high Reynolds numbers and provide directions for tuning the parameters involved in the model. For the implementation, we consider a three-step algorithm that we reformulate as an operator-splitting method. For the first time, this method is applied to a realistic problem of practical interest (flow in a nozzle). We carry out a successful validation against experimental measurements.

The *r*-ratio is a parameter that measures the local monotonicity, by which a number of high-resolution and TVD schemes can be formed. A number of *r*-ratio formulations for TVD schemes have been presented over the last few decades to solve the transport equation in shallow waters based on the finite volume method (FVM). However, unlike structured meshes, the coordinate directions are not clearly defined on an unstructured mesh; therefore, some *r*-ratio formulations have been established by approximating the solute concentration at virtual nodes, which may be estimated from different assumptions. However, some formulations may introduce either oscillation or diffusion behavior within the vertex-centered (VC) framework. In this paper, a new *r*-ratio formulation, applied to an unstructured grid in the VC framework, is proposed and compared with the traditional *r*-ratio formulations. Through seven commonly used benchmark tests, it is shown that the newly proposed *r*-ratio formulation obtains better results than the traditional ones with less numerical diffusion and spurious oscillation. Moreover, three commonly used TVD schemes—SUPERBEE, MINMOD, and MUSCL—and two high-order schemes—SOU and QUICK—are implemented and compared using the new *r*-ratio formulation. The new *r*-ratio formulation is shown to be sufficiently comprehensive to permit the general implementation of a high-resolution scheme within the VC framework. Finally, the sensitivity test for different grid types demonstrates the good adaptability of this new *r*-ratio formulation. Copyright © 2015 John Wiley & Sons, Ltd.

This paper presents a new r-ratio formulation for TVD schemes for vertex-centered finite volume method on an unstructured mesh. Through several numerical tests as shown later (concentration along x-axis in test of a spot moving in a rotating flow field), the new formulation has higher accuracy and less oscillations than traditional formulations, while it demonstrates a good adaptability to different unstructured meshes.

A three-dimensional numerical model is developed to analyze free surface flows and water impact problems. The flow of an incompressible viscous fluid is solved using the unsteady Navier–Stokes equations. Pseudo-time derivatives are introduced into the equations to improve computational efficiency. The interface between the two phases is tracked using a volume-of-fluid interface tracking algorithm developed in a generalized curvilinear coordinate system. The accuracy of the volume-of-fluid method is first evaluated by the multiple numerical benchmark tests, including two-dimensional and three-dimensional deformation cases on curvilinear grids. The performance and capability of the numerical model for water impact problems are demonstrated by simulations of water entries of the free-falling hemisphere and cone, based on comparisons of water impact loadings, velocities, and penetrations of the body with experimental data. For further validation, computations of the dam-break flows are presented, based on an analysis of the wave front propagation, water level, and the dynamic pressure impact of the waves on the downstream walls, on a specific container, and on a tall structure. Extensive comparisons between the obtained solutions, the experimental data, and the results of other numerical simulations in the literature are presented and show a good agreement. Copyright © 2015 John Wiley & Sons, Ltd.

A robust numerical solver based on the pseudo-compressibility Navier–Stokes model and the volume-of-fluid interface tracking method was developed for three-dimensional simulation of complex, free surface, and water impact flows. The proposed method is implemented using a generalized curvilinear coordinate system to facilitate complex, arbitrary simulations of the flows in practical problems. Several example computations concerning the numerical resolution, stability, and important physical characteristics of hydraulic and hydrodynamic problems exhibit a very good agreement with experimental and numerical data published in the literature.

The main contribution of this work is to classify the solution region including data extrema for which high-order non-oscillatory approximation can be achieved. It is performed in the framework of local maximum principle (LMP) and non-conservative formulation. The representative uniformly second-order accurate schemes are converted in to their non-conservative form using the ratio of consecutive gradients. Using the local maximum principle, these non-conservative schemes are analyzed for their non-linear LMP/total variation diminishing stability bounds which classify the solution region where high-order accuracy can be achieved. Based on the bounds, second-order accurate hybrid numerical schemes are constructed using a shock detector. The presented numerical results show that these hybrid schemes preserve high accuracy at non-sonic extrema without exhibiting any induced local oscillations or clipping error. Copyright © 2015 John Wiley & Sons, Ltd.

Using a local maximum principle, the solution region of hyperbolic scalar conservation law is classified into sub-regions where at least second-order non-oscillatory approximation can be achieved. Nonlinear stability bounds are given, which ensure for non-occurrence of induced oscillations by second-order schemes. Using these bounds, second-order accurate hybrid numerical schemes are constructed with the help of a shock detector, which can preserve high accuracy at non-sonic extrema without exhibiting any induced local oscillations or clipping error.

In this work, we present a high-order discontinuous Galerkin method (DGM) for simulating variable density flows at low Mach numbers. The corresponding low Mach number equations are an approximation of the compressible Navier–Stokes equations in the limit of zero Mach number. To the best of the authors'y knowledge, it is the first time that the DGM is applied to the low Mach number equations. The mixed-order formulation is applied for spatial discretization. For steady cases, we apply the semi-implicit method for pressure-linked equation (SIMPLE) algorithm to solve the non-linear system in a segregated manner. For unsteady cases, the solver is implicit in time using backward differentiation formulae, and the SIMPLE algorithm is applied to solve the non-linear system in each time step. Numerical results for the following three test cases are shown: Couette flow with a vertical temperature gradient, natural convection in a square cavity, and unsteady natural convection in a tall cavity. Considering a fixed number of degrees of freedom, the results demonstrate the benefits of using higher approximation orders. Copyright © 2015 John Wiley & Sons, Ltd.

We present a high-order discontinuous Galerkin method for simulating variable density flows at low Mach numbers. The solver is based on the lowMach number equations, which are an approximation of the compressible Navier–Stokes equations in the limit of zero Mach number. Numerical tests for Couette flow with a vertical temperature gradient and natural convection in enclosed cavities confirm the high accuracy of the method.

When a block factorisation is used to precondition the saddle-point equations of the discrete Stokes problem, the stability that this gives for the relaxation of residual errors may not be conserved in the coarse-grid approximations (CGA) of algebraic multi-grid (AMG) solvers. If the same first-order interpolation is used in the inter-grid transfer operators for the scalar and the vector fields, the conditioning degrades with each coarsening step until eventually a critical coarsening is reached beyond which residual errors are no longer damped and will become divergent with any further coarsening. It is shown that by introducing the same block pre-conditioner as an integral part of the coarsening algorithm, stable smoothing can be maintained at all levels of the CGA. The pre-conditioning need only be applied at preselected grid levels, one immediately before the critical threshold and others beyond that level if required. Excessive complexity in the CGA is thereby avoided. The method is purely algebraic and may be used for both classical AMG solvers and for smoothed-aggregation AMG solvers. It should be applicable to other coupled vector and scalar fields in science and engineering that involve second-order (block-diagonal) and first-order (block-off-diagonal) discrete difference operators. Copyright © 2015 John Wiley & Sons, Ltd.

A method of stabilisation is proposed for fully-implicit, algebraic multi-grid, solutions of saddle-point, coupled-field, problems. Mesh-independent convergence is demonstrated for (A) smoothed-aggregation AMG and (B) classical AMG. The reduction/convergence factors, *ρ*, are independent of both the mesh resolution, *Q*, and the degree of coarsening, * χ*, in the AMG coarse-grid approximations.

We present a new reference smoothness indicator for third-order weighted essentially non-oscillatory scheme to recover its design-order convergence at critical points. This reference smoothness indicator, which involves both the candidate and global smoothness indicators in the weighted essentially non-oscillatory framework, is devised according to a sufficient condition on the weights for third-order convergence. The recovery of design-order is verified by standard tests. Meanwhile, numerical results demonstrate that the present reference smoothness indicator produces sharper representation of the discontinuity owing to the combined effects of larger weight assignment to the discontinuous stencils and convergence rate recovery. Copyright © 2015 John Wiley & Sons, Ltd.

A new reference smoothness indicator *τ*_{NP} is devised for the third-order weighted essentially non-oscillatory-NP3 scheme to recover its design-order convergence at critical points, by considering the nonlinear combination of the candidate and global smoothness indicators. The good matching between the numerical solutions of weighted essentially non-oscillatory-NP3 and third-order upwind scheme in solving the smooth extremum problem forcefully confirmed the recovery of design-order accuracy. Meanwhile, standard tests also verified the benefit of *τ*_{NP} in producing sharper representation of the discontinuity.

The accuracy of numerical simulations of free-surface flows depends strongly on the computation of geometric quantities like normal vectors and curvatures. This geometrical information is additional to the actual degrees of freedom and usually requires a much finer discretization of the computational domain than the flow solution itself. Therefore, the utilization of a numerical method, which uses standard functions to discretize the unknown function in combination with an enhanced geometry representation is a natural step to improve the simulation efficiency. An example of such method is the NURBS-enhanced finite element method (NEFEM), recently proposed by Sevilla *et al*. The current paper discusses the extension of the spatial NEFEM to space-time methods and investigates the application of space-time NURBS-enhanced elements to free-surface flows. Derived is also a kinematic rule for the NURBS motion in time, which is able to preserve mass conservation over time. Numerical examples show the ability of the space-time NEFEM to account for both pressure discontinuities and surface tension effects and compute smooth free-surface forms. For these examples, the advantages of the NEFEM compared with the classical FEM are shown. Copyright © 2015 John Wiley & Sons, Ltd.

The paper at hand discusses the application of the recently proposed NURBS-enhanced finite element method (NEFEM) to free-surface flow simulations. In this context the 2D spatial NEFEM formulation is extended into the framework of space-time methods and a suitable kinematic rule for the NURBS motion in time is derived. The performance of the space-time NEFEM is compared to the standard FEM and the ability to preserve mass conservation over time is confirmed.

In this paper, we consider edge-based reconstruction (EBR) schemes for solving the Euler equations on unstructured tetrahedral meshes. These schemes are based on a high-accuracy quasi-1D reconstruction of variables on an extended stencil along the edge-based direction. For an arbitrary tetrahedral mesh, the EBR schemes provide higher accuracy in comparison with most second-order schemes at rather low computational costs. The EBR schemes are built in the framework of vertex-centered formulation for the point-wise values of variables.

Here, we prove the high accuracy of EBR schemes for uniform grid-like meshes, introduce an economical implementation of quasi-one-dimensional reconstruction and the resulting new scheme of EBR family, estimate the computational costs, and give new verification results. Copyright © 2015 John Wiley & Sons, Ltd.

The paper considers edge-based reconstruction (EBR) schemes for solving the Euler equations on unstructured tetrahedral meshes. These are vertex-centered schemes for the point-wise values that exploit a high-accuracy quasi-one-dimensional reconstruction of variables on an extended stencil along the edge-based direction. We prove the high accuracy of EBR schemes for uniform grid-like meshes, introduce their economical implementation, and compare them with the polynomial-based finite-volume schemes and flux corrector method.

The representation of geometries as buildings, flood barriers or dikes in free surface flow models implies tedious and time-consuming operations in order to define accurately the shape of these objects when using a body fitted numerical mesh. The immersed boundary method is an alternative way to define solid bodies inside the computational domain without the need of fitting the mesh boundaries to the shape of the object. In the direct forcing immersed boundary method, a solid body is represented by a grid of Lagrangian markers, which define its shape and which are independent from the fluid Eulerian mesh. This paper presents a new implementation of the immersed boundary method in an unstructured finite volume solver for the 2D shallow water equations. Moving least-squares is used to transmit information between the grid of Lagrangian markers and the fluid Eulerian mesh. The performance of the proposed implementation is analysed in three test cases involving different flow conditions: the flow around a spur dike, a dam break flow with an isolated obstacle and the flow around an array of obstacles. A very good agreement between the classic body fitted approach and the immersed boundary method was found. The differences between the results obtained with both methods are less relevant than the errors because of the intrinsic shallow water assumptions. Copyright © 2015 John Wiley & Sons, Ltd.

An immersed boundary method for use on unstructured meshes is proposed, with particular focus on its application to depth averaged shallow water models. Moving least-squares is used to generate the interpolation functions. The method is applied to the flow around a spur dike, a dam break with an isolated obstacle and the flow around an array of obstacles, and results are compared with simulations using classic body fitted meshes and experimental data. Good agreement is found between the numerical methods.

Two-dimensional flows past a stationary circular cylinder near a plane boundary are numerically simulated using an immersed interface method with second-order accuracy. Instead of a fixed wall, a moving wall with no-slip boundary is considered to avoid the complex involvement of the boundary layer and to focus only on the shear-free wall proximity effects for investigating the force dynamics and flow fields. To analyze the convergence and accuracy of our implementation, numerical studies have been first performed on a simple test problem of rotational flow, where the second order of convergence is confirmed through numerical experiments and an optimal range of relative grid-match ratio of Lagrangian to Eulerian grid sizes has been recommended. By comparing the force quantities and the Strouhal number, the accuracy of this method has been demonstrated on the flow past a stationary isolated cylinder. The cylinder is then put in proximity to the wall to investigate the shear-free wall proximity effects in the low Reynolds number regime (20≤*R**e*≤200). The gap ratio, *e*/*D*, where *e* denotes the gap between the cylinder and the moving wall and *D* denotes the diameter of the cylinder, is taken from 0.10 to 2.00 to determine the critical gap ratio, (*e*/*D*)_{critical}, for the alternate vortex shedding, where the fluid forces, flow fields and the streamwise velocity profiles are studied. One of the key findings is that the (*e*/*D*)_{critical} for the alternate vortex shedding decreases as the Reynolds number increases. We also find that, in this low Reynolds number regime, the mean drag coefficient increases and peaks at *e*/*D* = 0.5 with the increase of *e*/*D* and keeps decreasing gently from *e*/*D* = 0.5 to *e*/*D* = 2.0, while the mean lift coefficient decreases monotonically with the increase of *e*/*D*. New correlations are then proposed for computing force coefficients as a function of *R**e* and *e*/*D* for a cylinder in the vicinity of a moving plane wall. Copyright © 2015 John Wiley & Sons, Ltd.

Immersed interface method has been employed to study the shear-free wall proximity effects in the low Reynolds number regime (20≤Re≤200), where the hydrodynamic forces and the critical gap ratio for vortex shedding suppression are investigated. We have found that the mean drag coefficient, *C*_{D}, increases and peaks at ^{e}/_{D}=0.5 with the increase of ^{e}/_{D} and keeps decreasing gently from ^{e}/_{D}=0.5 to 2.0, while the mean lift coefficient, *C*_{L}, decreases monotonically with the increase of ^{e}/_{D} . With the consistent trends of force coefficients, new correlations have been proposed for the lift and drag coefficients as a function of ^{e}/_{D} and *R**e*.

An improved incompressible smoothed particle hydrodynamics (ISPH) method is presented, which employs first-order consistent discretization schemes both for the first-order and second-order spatial derivatives. A recently introduced wall boundary condition is implemented in the context of ISPH method, which does not rely on using dummy particles and, as a result, can be applied more efficiently and with less computational complexity. To assess the accuracy and computational efficiency of this improved ISPH method, a number of two-dimensional incompressible laminar internal flow benchmark problems are solved and the results are compared with available analytical solutions and numerical data. It is shown that using smaller smoothing lengths, the proposed method can provide desirable accuracies with relatively less computational cost for two-dimensional problems. Copyright © 2015 John Wiley & Sons, Ltd.

A consistent Incompressible smoothed particle hydrodynamics (ISPH) method is presented. The method employs first-order consistent discretization schemes for both the first-order and secondorder spatial derivatives and benefits from a robust boundary condition implementation. It is shown that for the range of two-dimensional incompressible laminar internal flow problems studied in this work, the proposed algorithm is more accurate and computationally more efficient compared with its standard ISPH counterpart.

The kernel gradient free (KGF) smoothed particle hydrodynamics (SPH) method is a modified finite particle method (FPM) which has higher order accuracy than the conventional SPH method. In KGF-SPH, no kernel gradient is required in the whole computation, and this leads to good flexibility in the selection of smoothing functions and it is also associated with a symmetric corrective matrix. When modeling viscous incompressible flows with SPH, FPM or KGF-SPH, it is usual to approximate the Laplacian term with nested approximation on velocity, and this may introduce numerical errors from the nested approximation, and also cause difficulties in dealing with boundary conditions. In this paper, an improved KGF-SPH method is presented for modeling viscous, incompressible fluid flows with a novel discrete scheme of Laplacian operator. The improved KGF-SPH method avoids nested approximation of first order derivatives, and keeps the good feature of ‘kernel gradient free’. The two-dimensional incompressible fluid flow of shear cavity, both in Euler frame and Lagrangian frame, are simulated by SPH, FPM, the original KGF-SPH and improved KGF-SPH. The numerical results show that the improved KGF-SPH with the novel discrete scheme of Laplacian operator are more accurate than SPH, and more stable than FPM and the original KGF-SPH. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, an improved kernel gradient free (KGF)-smoothed particle hydrodynamics (SPH) method with a novel discrete scheme of Laplacian operator is presented for modeling viscous, incompressible fluid flows. Improved KGF-SPH method avoids nested approximation of first-order derivatives, and keeps the good feature of ‘KGF’. The 2D incompressible flows of lid-driven shear cavity, both in Euler frame and Lagrangian frame, are simulated by SPH, FPM, original and improved KGF-SPH. As shown in the figure (pressure coefficient profiles along upper wall for a lid-driven shear cavity problem), improved KGF-SPH with the novel discrete scheme of Laplacian operator is more accurate and stable than SPH, FPM and original KGF-SPH.

An integrated finite element method (FEM) is proposed to simulate incompressible two-phase flows with surface tension effects, and three different surface tension models are applied to the FEM to investigate spurious currents and temporal stability. A Q2Q1 element is adopted to solve the continuity and Navier–Stokes equations and a Q2-iso-Q1 to solve the level set equation. The integrated FEM solves pressure and velocity simultaneously in a strongly coupled manner; the level set function is reinitialized by adopting a direct approach using interfacial geometry information instead of solving a conventional hyperbolic-type equation. In addition, a consistent continuum surface force (consistent CSF) model is utilized by employing the same basis function for both surface tension and pressure variables to damp out spurious currents and to estimate the accurate pressure distribution. The model is further represented as a semi-implicit manner to improve temporal stability with an increased time step. In order to verify the accuracy and robustness of the code, the present method is applied to a few benchmark problems of the static bubble and rising bubble with large density and viscosity ratios. The Q2Q1-integrated FEM coupled with the semi-implicit consistent CSF demonstrates the significantly reduced spurious currents and improved temporal stability. The numerical results are in good qualitative and quantitative agreements with those of the existing studies. Copyright © 2015 John Wiley & Sons, Ltd.

In finite element method, a consistent continuum surface force model is introduced by employing the same basis function for both surface tension and pressure variables to damp out spurious currents and to estimate the accurate pressure distribution. The model is further represented as a semi-implicit manner to improve temporal stability with an increased time step. The Q2Q1 integrated FEM coupled with the semi-implicit consistent CSF demonstrates the significantly reduced spurious currents and improved temporal stability.

An embedded formulation for the simulation of immiscible multi-fluid problems is proposed. The method is particularly designed for handling gas–liquid systems. Gas and liquid are modeled using the Eulerian and the Lagrangian formulation, respectively. The Lagrangian domain (liquid) moves on top of the fixed Eulerian mesh. The location of the material interface is exactly defined by the position of the boundary mesh of the Lagrangian domain. The individual fluid problems are solved in a partitioned fashion and are coupled using a Dirichlet–Neumann algorithm. Representation of the pressure discontinuity across the interface does not require any additional techniques being an intrinsic feature of the method. The proposed formulation is validated, and its potential applications are shown. Copyright © 2015 John Wiley & Sons, Ltd.

Gas-liquid systems can be efficiently modeled in a partitioned embedded fashion adopting fixed mesh (Eulerian) approach for the gas and mesh-moving one (Lagrangian) for the liquid. The interface tracking and flow variables' discontinuity across the interface becomes thus a natural feature of the method. Surface tension is applied on the mesh-defined boundary of the liquid phase. The main strength of the approach is the full control over the coupling strength between the sub-domains, allowing for both weak and fully coupled algorithms.

A high-order difference method based multiphase model is proposed to simulate nonlinear interactions between water wave and submerged coastal structures. The model is based on the Navier–Stokes equations using a constrained interpolation profile (CIP) method for the flow solver, and employs an immersed boundary method (IBM) for the treatment of wave–structure interactions. A more accurate interface capturing scheme, the volume of fluid/weighed line interface calculation (VOF/WLIC) scheme, is adopted as the interface capturing method. A series of computations are performed to verify the application of the model for simulations of fluid interaction with various structures. These problems include flow over a fixed cylinder, water entry of a circular cylinder and solitary waves passing various submerged coastal structures. Computations are compared with the available analytical, experimental and other numerical results and good agreement is obtained. The results of this study demonstrate the accuracy and applications of the proposed model to simulate the nonlinear flow phenomena and capture the complex free surface flow. Copyright © 2015 John Wiley & Sons, Ltd.

Numerical simulations of water wave interaction with coastal structures are performed by an improved CIP-based Cartesian grid method, in which a more accurate interface capturing scheme is combined for the free surface capturing and the immersed boundary method for the solid boundary treatment. Computations are compared with available analytical, experimental and other numerical results. The present model proves to be a promising tool for simulation of coastal engineering applications with acceptable accuracy.

The mass-conserving level-set (MCLS) method is a hybrid level-set (LS)/volume of fluid (VoF) based, interface capturing algorithm that combines the mass conserving properties of the VoF, with the benefits of having an explicit description of the interface of the LS method. The efficiency of the method is a result of the fact that the LS formulation allows evaluation of the VoF-field and VoF-fluxes without reconstruction of the interface in each cell. We present the extension of the MCLS method from its original formulation for Cartesian quadrilateral control volumes to triangular control volumes for optimal geometrical flexibility. The LS field is discretized using a second order discontinuous Galerkin method. After each time-step, a mass-conserving correction is imposed based on the simultaneously convected VoF field. This convection step is performed with a second-order Eulerian–Lagrangian approach, combined with a ‘clipping’ algorithm to project the advected field from the Lagrangian to the Eulerian grid. The MCLS method is shown to be accurately mass conserving and shows second order convergence for three different test cases. Copyright © 2015 John Wiley & Sons, Ltd.

We present the extension of the MCLS method toward unstructured triangular grids for two phase flow. The VoF function and the inverse function derived for a triangular mesh are very simple, robust and efficient to evaluate. Our approach is significantly more efficient and robust than the original MCLS formulation. Numerical experiments indicate the LS field converges with second order accuracy in space and mass is conserved up to machine precision.

In this paper, we develop a new hybrid Euler flux function based on Roe's flux difference scheme, which is free from shock instability and still preserves the accuracy and efficiency of Roe's flux scheme. For computational cost, only 5*%* extra CPU time is required compared with Roe's FDS. In hypersonic flow simulation with high-order methods, the hybrid flux function would automatically switch to the Rusanov flux function near shock waves to improve the robustness, and in smooth regions, Roe's FDS would be recovered so that the advantages of high-order methods can be maintained. Multidimensional dissipation is introduced to eliminate the adverse effects caused by flux function switching and further enhance the robustness of shock-capturing, especially when the shock waves are not aligned with grids. A series of tests shows that this new hybrid flux function with a high-order weighted compact nonlinear scheme is not only robust for shock-capturing but also accurate for hypersonic heat transfer prediction. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we develop a very robust hybrid flux function to overcome the shock instability in hypersonic flow simulation with high-order methods. Multidimensional dissipation and entropy correction based on local flow field are introduced to enhance the robustness and resolution of the hybrid flux function. A series of tests shows that this new hybrid flux function with a fifth-order weighted compact nonlinear scheme (WCNS) is not only robust for shock-capturing but also accurate for hypersonic heat transfer prediction.

Currently, the majority of computational fluid dynamics (CFD) codes use the finite volume method to spatially discretise the computational domain, sometimes as an array of cubic control volumes. The Finite volume method works well with single-phase flow simulations, but two-phase flow simulations are more challenging because of the need to track the surface interface traversing and deforming within the 3D grid. Surface area and volume fraction details of each interface cell must be accurately accounted for, in order to calculate for the momentum exchange and rates of heat and mass transfer across the interface. To attain a higher accuracy in two-phase flow CFD calculations, the intersection marker (ISM) method is developed. The ISM method is a hybrid Lagrangian–Eulerian front-tracking algorithm that can model an arbitrary 3D surface within an array of cubic control volumes. The ISM method has a cell-by-cell remeshing capability that is volume conservative and is suitable for the tracking of complex interface deformation in transient two-phase CFD simulations. Copyright © 2015 John Wiley & Sons, Ltd.

The intersection marker method is a novel approach for modelling an arbitrary 3D surface within an array of cubic control volumes. Intersection marker's novelty lies in its ability to remesh the interface on a cell-by-cell basis whilst maintaining surface continuity and local volume conservation without the use of permanent surface markers.

We optimized the Arbitrary accuracy DErivatives Riemann problem (ADER) - Discontinuous Galerkin (DG) numerical method using the CUDA-C language to run the code in a graphic processing unit (GPU). We focus on solving linear hyperbolic partial–differential equations where the method can be expressed as a combination of precomputed matrix multiplications becoming a good candidate to be used on the GPU hardware. Moreover, the method is arbitrarily high order involving intensive work on local data, a property that is also beneficial for the target hardware. We compare our GPU implementation against CPU versions of the same method observing similar convergence properties up to a threshold where the error remains fixed. This behavior is in agreement with the CPU version, but the threshold is slightly larger than in the CPU case. We also observe a big difference when considering single and double precisions where in the first case, the threshold error is significantly larger. Finally, we did observe a speed-up factor in computational time that depends on the order of the method and the size of the problem. In the best case, our novel GPU implementation runs 23 times faster than the CPU version. We used three partial–differential equation to test the code considering the linear advection equation, the seismic wave equation, and the linear shallow water equation, all of them considering variable coefficients. Copyright © 2015 John Wiley & Sons, Ltd.

In the figure, we show a convergence test considering the 2D linear elastic wave equation. We compare double precision and single precision of the graphics processor unit implementation against the CPU code SeisSol for different orders from second (P1) to sixth (P5). In the vertical axis, the error level is obtained using the L_2 norm. The figure on the left depicts the error against mesh size, while on the right, the horizontal axis represents computational time.

An unstructured, shock-fitting algorithm, originally developed to simulate steady flows, has being further developed to make it capable of dealing with unsteady flows. The present paper discusses and analyses the additional features required to extend to unsteady flows, the steady algorithm. The properties of the unsteady version of this novel, unstructured shock-fitting technique, are tested by reference to the inviscid interaction between a vortex and a planar shock: a comparative assessment of shock-capturing and shock-fitting is made for the same test problem. Copyright © 2015 John Wiley & Sons, Ltd.

An unstructured, shock-fitting algorithm, originally developed to simulate steady flows, has been further developed to make it capable of dealing with unsteady flows. The present paper discusses and analyses the additional features required to extend to unsteady flows the steady algorithm.

The method for computation of stability modes for two- and three-dimensional flows is presented. The method is based on the dynamic mode decomposition of the data resulting from DNS of the flow in the regime close to stable flow (fixed-point dynamics, small perturbations about steady flow). The proposed approach is demonstrated on the wake flows past a 2D, circular cylinder, and a sphere. The resulting modes resemble the eigenmodes computed conventionally from global stability analysis and are used in model order reduction of the flow. The designed low-dimensional Galerkin model uses continuous mode interpolation between dynamic mode decomposition mode bases and reproduces the dynamics of Navier–Stokes equations. Copyright © 2015 John Wiley & Sons, Ltd.

The method for computation of stability modes for two- and three-dimensional flows is presented. The method bases on the Dynamic Mode Decomposition of the data resulting from Direct Numerical Simulation of the flow in the regime close to steady flow. The resulting modes resemble the eigenmodes of global stability analysis and are used to design low dimensional Galerkin models of theflow.

In this work, an approach is proposed for solving the 3D shallow water equations with embedded boundaries that are not aligned with the underlying horizontal Cartesian grid. A hybrid cut-cell/ghost-cell method is used together with a direction-splitting implicit solver: Ghost cells are used for the momentum equations in order to prescribe the correct boundary condition at the immersed boundary, while cut cells are used in the continuity equation in order to conserve mass. The resulting scheme is robust, does not suffer any time step limitation for small cut cells, and conserves fluid mass up to machine precision. Moreover, the solver displays a second-order spatial accuracy, both globally and locally. Comparisons with analytical solutions and reference numerical solutions on curvilinear grids confirm the quality of the method. Copyright © 2015 John Wiley & Sons, Ltd.

An immersed boundary model for shallow water equations based on a staggered alternating direction implicit solver is proposed. The scheme is implicit, and therefore, the time step is not constrained by the Courant–Friedrichs–Lewy condition. The model accurately describes 2D and 3D flow in both straight and curved channels.

This paper introduces a vertex-centered linearity-preserving finite volume scheme for the heterogeneous anisotropic diffusion equations on general polygonal meshes. The unknowns of this scheme are purely the values at the mesh vertices, and no auxiliary unknowns are utilized. The scheme is locally conservative with respect to the dual mesh, captures exactly the linear solutions, leads to a symmetric positive definite matrix, and yields a nine-point stencil on structured quadrilateral meshes. The coercivity of the scheme is rigorously analyzed on arbitrary mesh size under some weak geometry assumptions. Also, the relation with the finite volume element method is discussed. Finally, some numerical tests show the optimal convergence rates for the discrete solution and flux on various mesh types and for various diffusion tensors. Copyright © 2015 John Wiley & Sons, Ltd.

The new vertex-centered scheme possesses the three properties: the local conservation, the symmetry and positive definiteness, and the linearity preserving (preserve the linear solution exactly), which is rarely seen in the existing cell-centered or vertex-centered scheme. The coercivity of the scheme is rigorously analyzed on arbitrary mesh size under some weak geometry assumptions. Several numerical tests show that the new scheme has approximately second-order accuracy on general polygonal meshes.

This paper describes a numerical discretization of the compressible Euler equations with a gravitational potential. A pertinent feature of the solutions to these inhomogeneous equations is the special case of stationary solutions with zero velocity, described by a nonlinear partial differential equation, whose solutions are called hydrostatic equilibria. We present a well-balanced method, meaning that besides discretizing the complete equations, the method is also able to maintain all hydrostatic equilibria. The method is a finite volume method, whose Riemann solver is approximated by a so-called relaxation Riemann solution that takes all hydrostatic equilibria into account. Relaxation ensures robustness, accuracy, and stability of our method, because it satisfies discrete entropy inequalities. We will present numerical examples, illustrating that our method works as promised. Copyright © 2015 John Wiley & Sons, Ltd.

We present a finite volume scheme to approximate the Euler equations with a gravitational source term based on a relaxation method. A particular attention is paid on the preservation of the hydrostatic steady-state solutions of the system. Moreover, the scheme is also proven to be robust and entropy preserving.

This paper presents a coupled finite volume inner doubly iterative efficient algorithm for linked equations (IDEAL) with level set method to simulate the incompressible gas–liquid two-phase flows with moving interfaces on unstructured triangular grid. The finite volume IDEAL method on a collocated grid is employed to solve the incompressible two-phase Navier–Stokes equations, and the level set method is used to capture the moving interfaces. For the sake of mass conservation, an effective second-order accurate finite volume scheme is developed to solve the level set equation on triangular grid, which can be implemented much easier than the classical high-order level set solvers. In this scheme, the value of level set function on the boundary of control volume is approximated using a linear combination of a high-order Larangian interpolation and a second-order upwind interpolation. By the rotating slotted disk and stretching and shrinking of a circular fluid element benchmark cases, the mass conservation and accuracy of the new scheme is verified. Then the coupled method is applied to two-phase flows, including a 2D bubble rising problem and a 2D dam breaking problem. The computational results agree well with those reported in literatures and experimental data. Copyright © 2015 John Wiley & Sons, Ltd.

This paper develops a new finite volume scheme for solving the level set equation. The new scheme can preserve the mass conservation accurately in level set method.

The present article concerns a commonly used methodology for the numerical simulation of acoustic emission and propagation phenomena. We consider the so-called multi-stage hybrid acoustic approach, in which a given noise problem is simulated via a sequence of weakly coupled computations of noise generation and acoustic propagation stages, wherein the simulation of the propagation stage is based on advanced Computational AeroAcoustics (CAA) techniques. The paper introduces an original forcing technique, namely, the Non-Reflective Interface (NRI), to enable the transfer of an acoustic signal from an a priori noise generation stage into a CAA-based acoustic propagation phase. Unlike most existing forcing techniques, the NRI is non-reflective (or anechoic) in nature and, therefore, can properly handle the backscattering effects arising during the noise propagation stage. This attribute makes the NRI-based weak-coupling procedure and the associated CAA-based hybrid approach compatible with a larger variety of realistic noise problems (such as those involving installed configurations in wind tunnel experiments, for instance). The NRI technique is first validated via several test cases of increasing complexity and is then applied to two aerodynamic noise problems. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Regarding those hybrid methods in acoustics for which the propagation stage is based on advanced Computational AeroAcoustics (CAA) techniques, the present article introduces an original forcing technique, namely, the Non-Reflective Interface (NRI), to enable the transfer of an acoustic signal from an a priori noise generation stage into a CAA-based acoustic propagation phase. Unlike most existing forcing techniques, the NRI makes the associated CAA-based hybrid approach compatible with a large variety of realistic noise problems.

In this paper, we propose a model based on a new contravariant integral form of the fully nonlinear Boussinesq equations in order to simulate wave transformation phenomena, wave breaking, and nearshore currents in computational domains representing the complex morphology of real coastal regions. The aforementioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. A procedure developed in order to correct errors related to the difficulties of numerically satisfying the metric identities in the numerical integration of fully nonlinear Boussinesq equation on generalized boundary-conforming grids is presented. The Boussinesq equation system is numerically solved by a hybrid finite volume–finite difference scheme. The proposed high-order upwind weighted essentially non-oscillatory finite volume scheme involves an exact Riemann solver and is based on a genuinely two-dimensional reconstruction procedure, which uses a convex combination of biquadratic polynomials. The wave breaking is represented by discontinuities of the weak solution of the integral form of the nonlinear shallow water equations.

The capacity of the proposed model to correctly represent wave propagation, wave breaking, and wave-induced currents is verified against test cases present in the literature. The results obtained are compared with experimental measures, analytical solutions, or alternative numerical solutions. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we propose a model based on a new contravariant integral form of fully nonlinear Boussinesq equations in order to simulate wave transformation phenomena, wave breaking, and near shore currents in computational domains representing the complex morphology of real coastal regions. The aforementioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. We propose an original shock-capturing scheme, for the numerical integration of the fully nonlinear Boussinesq equation, which is based on a genuinely two-dimensional weighted essentially non-oscillatory reconstruction procedure. It has been demonstrated that the presented Boussinesq model can be used for the simulation of wave fields and nearshore currents in the coastal region characterized by morphologically complex coastal lines and irregular seabeds and by the presence of maritime infrastructures.

This paper presents a simple finite element method for Stokes flows with surface tension. The method uses an unfitted mesh that is independent of the interface. Due to the surface force, the pressure has a jump across the interface. Based on the properties of the level set function that implicitly represents the interface, the jump of the pressure is removed, and a new problem without discontinuities is formulated. Then, classical stable finite element methods are applied to solve the new problem. Some techniques are used to show that the method is equivalent to an easy-to-implement method that can be regarded as a traditional method with a modified pressure space. However, the matrix of the resulting linear system of equations is the same as that of the traditional method. Optimal error estimates are derived for the proposed method. Finally, some numerical tests are presented to confirm the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.

For the static three-dimensional bubble, the proposed method reduces the oscillations near the interface substantially. Note that coefficient matrix of the resulting system of the proposed method is the same as that of the traditional FEM.

A modification of the Roe scheme called L^{2}Roe for low dissipation low Mach Roe is presented. It reduces the dissipation of kinetic energy at the highest resolved wave numbers in a low Mach number test case of decaying isotropic turbulence. This is achieved by scaling the jumps in all discrete velocity components within the numerical flux function. An asymptotic analysis is used to show the correct pressure scaling at low Mach numbers and to identify the reduced numerical dissipation in that regime. Furthermore, the analysis allows a comparison with two other schemes that employ different scaling of discrete velocity jumps, namely, LMRoe and a method of Thornber *et al.* To this end, we present for the first time an asymptotic analysis of the last method. Numerical tests on cases ranging from low Mach number (*M*_{∞}=0.001) to hypersonic (*M*_{∞}=5) viscous flows are used to illustrate the differences between the methods and to show the correct behavior of L^{2}Roe. No conflict is observed between the reduced numerical dissipation and the accuracy or stability of the scheme in any of the investigated test cases. Copyright © 2015 John Wiley & Sons, Ltd.

A modification of the Roe scheme is discussed that improves the dissipation of kinetic energy at the highest resolved wave numbers in a low Mach number test case of decaying isotropic turbulence. This is performed by scaling the jumps in all discrete velocity components within the numerical flux function. An asymptotic analysis is used to show the correct pressure scaling at low Mach numbers and to identify the reduced numerical dissipation in that regime, both of the new method L2Roe and the two other methods previously suggested by other authors.

In both bubbly and porous media flow, the jumps in coefficients may yield an ill-conditioned linear system. The solution of this system using an iterative technique like the conjugate gradient (CG) is delayed because of the presence of small eigenvalues in the spectrum of the coefficient matrix. To accelerate the convergence, we use two levels of preconditioning. For the first level, we choose between out-of-the-box incomplete LU decomposition, sparse approximate inverse, and truncated Neumann series-based preconditioner. For the second level, we use deflation. Through our experiments, we show that it is possible to achieve a computationally fast solver on a graphics processing unit. The preconditioners discussed in this work exhibit fine-grained parallelism. We show that the graphics processing unit version of the two-level preconditioned CG can be up to two times faster than a dual quad core CPU implementation. John Wiley & Sons, Ltd.

In this work, we present the implementation of the deflated preconditioned conjugate gradient method on the GPU using PARALUTION. Through our experiments with two different problems, we prove that it is advantageous to use this method in comparison with optimized CPU implementations of preconditioned CG methods.

The discontinuous Galerkin (DG) transport scheme is becoming increasingly popular in the atmospheric modeling due to its distinguished features, such as high-order accuracy and high-parallel efficiency. Despite the great advantages, DG schemes may produce unphysical oscillations in approximating transport equations with discontinuous solution structures including strong shocks or sharp gradients. Nonlinear limiters need to be applied to suppress the undesirable oscillations and enhance the numerical stability. It is usually very difficult to design limiters to achieve both high-order accuracy and non-oscillatory properties and even more challenging for the cubed-sphere geometry. In this paper, a simple and efficient limiter based on the weighted essentially non-oscillatory (WENO) methodology is incorporated in the DG transport framework on the cubed sphere. The uniform high-order accuracy of the resulting scheme is maintained because of the high-order nature of WENO procedures. Unlike the classic WENO limiter, for which the wide halo region may significantly impede parallel efficiency, the simple limiter requires only the information from the nearest neighboring elements without degrading the inherent high-parallel efficiency of the DG scheme. A bound-preserving filter can be further coupled in the scheme that guarantees the highly desirable positivity-preserving property for the numerical solution. The resulting scheme is high-order accurate, non-oscillatory, and positivity preserving for solving transport equations based on the cubed-sphere geometry. Extensive numerical results for several benchmark spherical transport problems are provided to demonstrate good results, both in accuracy and in non-oscillatory performance. Copyright © 2015 John Wiley & Sons, Ltd.

A simple and efficient limiter based on the weighted essentially non-oscillatory methodology is incorporated in the discontinuous Galerkin transport framework on the cubed sphere, with the following distinctive features: high-order accurate, good non-oscillatory properties, easy to implement, and can avoid ghost cells when applied to a corner cell of the cubed sphere.

A novel parallel monolithic algorithm has been developed for the numerical simulation of large-scale fluid structure interaction problems. The governing incompressible Navier–Stokes equations for the fluid domain are discretized using the arbitrary Lagrangian–Eulerian formulation-based side-centered unstructured finite volume method. The deformation of the solid domain is governed by the constitutive laws for the nonlinear Saint Venant–Kirchhoff material, and the classical Galerkin finite element method is used to discretize the governing equations in a Lagrangian frame. A special attention is given to construct an algorithm with exact total fluid volume conservation while obeying both the global and the local discrete geometric conservation law. The resulting large-scale algebraic nonlinear equations are multiplied with an upper triangular right preconditioner that results in a scaled discrete Laplacian instead of a zero block in the original system. Then, a one-level restricted additive Schwarz preconditioner with a block-incomplete factorization within each partitioned sub-domains is utilized for the modified system. The accuracy and performance of the proposed algorithm are verified for the several benchmark problems including a pressure pulse in a flexible circular tube, a flag interacting with an incompressible viscous flow, and so on. John Wiley & Sons, Ltd.

A novel FSI algorithm is proposed for the large-scale simulation of fluid-structure interaction problems in a fully coupled form. A special attention is given to satisfy both the local and global discrete geometric conservation law (DGCL) in order to conserve the total fluid volume/mass in machine precision. Large-scale numerical results are presented for several classical FSI benchmark problems.

A new numerical method for particle tracking (Lagrangian particle advection) on 2-D unstructured grids with triangular cells is presented and tested. This method combines key attributes of published methods, including streamline closure for steady flows and local mass conservation (uniformity preservation). The subgrid-scale velocity reconstruction is linear, and this linear velocity field is integrated analytically to obtain particle trajectories. A complete analytic solution to the 2-D system of ordinary differential equations (ODEs) governing particle trajectories within a grid cell is provided. The analytic solution to the linear system of locally mass-conserving constraints that must be enforced to obtain the coefficients in the ODEs is also provided. Numerical experiments are performed to demonstrate that the new method has substantial advantages in accuracy over previously published methods and that it does not suffer from unphysical particle clustering. The method can be used not only in particle-tracking applications but also as part of a semi-Lagrangian advection scheme.Copyright © 2015 John Wiley & Sons, Ltd.

We present a new 2-D Lagrangian particle-tracking method on triangular unstructured grids that is more accurate than previously published methods and does not suffer from unphysical particle clustering. We also present the complete analytic solution to the 2-D system of ordinary differential equations (ODEs) governing particle tracks, the analytic solution to the linear system of locally mass-conserving constraints used to obtain the coefficients in the ODEs, and numerical tests demonstrating the accuracy and mass-conserving property of the method.

We present a new modelling strategy for improving the efficiency of computationally intensive flow problems in environmental free-surface flows. The approach combines a recently developed semi-implicit subgrid method with a hierarchical grid solution strategy. The method allows the incorporation of high-resolution data on subgrid scale to obtain a more accurate and efficient hydrodynamic model. The subgrid method improves the efficiency of the hierarchical grid method by providing better solutions on coarse grids. The method is applicable to both steady and unsteady flows, but we particularly focus on river flows with steady boundary conditions. There, the combined hierarchical grid–subgrid method reduces the computational effort to obtain a steady state with factors up to 43. For unsteady models, the method can be used for efficiently generating accurate initial conditions on high-resolution grids. Additionally, the method provides automatic insight in grid convergence. We demonstrate the efficiency and applicability of the method using a schematic test for the vortex shedding around a circular cylinder and a real-world river case study.Copyright © 2015John Wiley & Sons, Ltd.

We present a semi-implicit method for free surface flows that incorporates high-resolution geometric data on subgrid level and applies a hierarchical grid solution strategy. The subgrid method makes sure that coarse-grid solutions within the hierarchical grid approach resemble the fine-grid solution, thereby considerably improving the efficiency and accuracy of the hydrodynamic model and providing automatic insight in grid convergence. A novel interpolation method that avoids the introduction of disturbances was applied to transfer data from coarse to fine grids.

Four-dimensional variational data assimilation (4DVAR) is frequently used to improve model forecasting skills. This method improves a model consistency with available data by minimizing a cost function measuring the model–data misfit with respect to some model inputs and parameters. Associated with this type of method, however, are difficulties related to the coding of the adjoint model, which is needed to compute the gradient of the 4DVAR cost function. Proper orthogonal decomposition (POD) is a model reduction method that can be used to approximate the gradient calculation in 4DVAR. In this work, two ways of using POD in 4DVAR are presented, namely model-reduced 4DVAR and reduced adjoint 4DVAR (RA-4DVAR). Both techniques employ POD to obtain a reduced-order approximation of the forward linear tangent operator. The difference between the two methods lies in the treatment of the forward model. Model-reduced 4DVAR performs minimization entirely in the POD-reduced space, thereby achieving very low computational costs, but sacrificing accuracy of the end result. On the other hand, the RA-4DVAR uses POD to approximate only the adjoint model. The main contribution of this study is a comparative performance analysis of these 4DVAR methodologies on a nonlinear finite element shallow water model. The sensitivity of the methods to perturbations in observations and the number of observation points is examined. The results from twin experiments suggest that the RA-4DVAR method is easy to implement and computationally efficient and provides a robust approach for achieving reasonable results in the context of variational data assimilation. Copyright © 2015 John Wiley & Sons, Ltd.

Four-dimensional variational data assimilation is frequently used to improve model forecasting skills. The method although requires computation of the gradient of the cost function, which requires huge programming burden to build the adjoint model. Here, comparative performance analysis on a nonlinear finite element shallow water model is performed using alternate four-dimensional variational data assimilation methodologies based on proper orthogonal decomposition. These approaches are nonintrusive in nature and do not require any modifications to system code; thus, they are very easy to implement.

Global linear stability analysis combined with computational fluid dynamics (CFD) is considered useful for understanding the physics of fluid flows. However, the numerical techniques of global linear stability analysis for compressible flows have not been well established in comparison with those for incompressible flows. In this study, we develop and assess a set of appropriate numerical techniques required to conduct a global linear stability analysis for compressible flows. For the eigensystem analysis, the Arnoldi method combined with time integration is in effect to preserve the memory (RAM) size of the computer. The compact difference scheme is used for the CFD analysis from the viewpoints of computing accurate global modes and saving memory by reducing the number of grid points to obtain the necessary spatial resolution. To assess the proposed method, two-dimensional compressible flow problems, including regularized cavity flow, flow around a square cylinder, and the compressible mixing layer, are analyzed, and it is confirmed that the proposed method can obtain accurate mode shapes, growth rate, and frequency of the corresponding global modes. In addition, influences and an appropriate formulation of the outflow boundary conditions are investigated. Results reveal that the outflow boundary causes spurious unstable modes in the global linear stability analysis, and the radiation and outflow boundary condition and the extension of the computational domain with grid stretching keep the spurious unstable modes to a minimum. Copyright © 2015 John Wiley & Sons, Ltd.

A set of numerical techniques for global linear stability analysis of compressible flows is developed and assessed. We demonstrated that the proposed method can accurately analyze the global stability of low and high subsonic Mach number flows and be performed with low memory consumption. Numerical experiments show that the outflow boundary causes spurious unstable modes and the radiation and outflow boundary condition and the extension of the computational domain with grid stretching keep the spurious unstable modes to a minimum.

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]]>In this work, we propose a novel approach to model order reduction for incompressible fluid flows, which focuses on the spatio-temporal description of the stresses on the surface of a body, that is, of the wall shear stress and of the wall pressure. The spatial representation of these two variables is given by a compact set of ‘wall basis functions’, that is, elementary basis functions defined on the wall. In this paper, these are derived using the well-known proper orthogonal decomposition to represent optimally the fluctuation energy of the pressure and shear stress. On the other hand, the functional structure of the dynamic model is derived from the first principles using the vorticity form of the Navier–Stokes equations, yielding a set of nonlinear ordinary differential equations for the time-varying amplitudes of the wall shear stress basis functions. Coefficients of this model are then identified from simulation data. To complete the system, we show that the surface pressure distribution, that is, the time-varying amplitudes of the wall pressure basis functions, can be derived from a quadratic model of the wall shear stress temporal coefficients, stemming from the Poisson equation for the pressure. This further step is crucial for the correct representation of the aerodynamic forces. As a paradigmatic example, we present our approach for the modelling of the free dynamics of the separated flow around a circular cylinder in the laminar regime, at *R**e* = 200. Further implications and potentialities of the proposed approach are discussed. Copyright © 2015 John Wiley & Sons, Ltd.

A novel approach for model order reduction for incompressible fluid flows is discussed. A compact set of elementary ‘wall basis functions’ is first derived via POD to provide a low-order representation of the spatial distribution of the surface stresses. A dynamical model, providing the temporal dynamics of the amplitudes of the wall structures, is then identified from data. The method is applied to the paradigmatic example of modelling the flow past a circular cylinder at **R****e** = 200.

This work presents an approximate Riemann solver to the transient isothermal drift**-**flux model. The set of equations constitutes a non-linear hyperbolic system of conservation laws in one space dimension. The elements of the Jacobian matrix **A** are expressed through exact analytical expressions. It is also proposed a simplified form of **A** considering the square of the gas to liquid sound velocity ratio much lower than one. This approximation aims to express the eigenvalues through simpler algebraic expressions. A numerical method based on the Gudunov's fluxes is proposed employing an upwind and a high order scheme. The Roe linearization is applied to the simplified form of **A**. The proposed solver is validated against three benchmark solutions and two experimental pipe flow data. Copyright © 2015 John Wiley & Sons, Ltd.

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This work presents an approximate Riemann solver to the transient isothermal drift-flux model. The set of equations constitutes a non-linear hyperbolic system of conservation laws in one space dimension. The elements of the Jacobian matrix A are expressed through exact analytical expressions. It is also proposed a simplified form of A considering the square of the gas to liquid sound velocity ratio much lower than one. This approximation aims to express the eigenvalues through simpler algebraic expressions. A numerical method based on the Gudunov's fluxes is proposed employing an upwind and a high order scheme. The Roe linearization is applied to the simplified form of A. The proposed solver is validated against three benchmark solutions and two experimental pipe flow data. Copyright © 2015 John Wiley & Sons, Ltd.