A novel conservative interpolation (remapping) method, in the Arbitrary Lagrangian–Eulerian context for numerical solution of Euler equations on unstructured polygonal grids, is presented. Combination of a piecewise quadratic reconstruction and a flux corrected remapping approach provides a simple, symmetry-preserving and bounds-preserving method. The positivity of density and specific internal energy is guaranteed. The complete description of the method and both cyclic remapping and full hydrodynamic 2D numerical examples are given. Copyright © 2014 John Wiley & Sons, Ltd.

A novel conservative interpolation method, in the Arbitrary Lagrangian-Eulerian context for numerical solution of Euler equations on unstructured polygonal grids, is presented. The positivity of density and specific internal energy is guaranteed. The complete description of the method and both cyclic remapping and full hydrodynamic two-dimensional numerical examples are given.

Lid-driven cavity flow at moderate Reynolds numbers is studied here, employing a mesh-free method known as Smoothed Particle Hydrodynamics (SPH). In a detailed study of this benchmark, the incompressible SPH approach is applied together with a particle shifting algorithm. Additionally, a new treatment for no-slip boundary conditions is developed and tested. The use of the aforementioned numerical treatment for solid walls leads to significant improvements in the results with respect to other SPH simulations carried out with similar spatial resolution. However, the effect of spatial resolution is not considered in the present study as the number of particles used in each case was kept constant, approximately reproducing the same resolutions employed in reference studies available in the literature as well. Altogether, the detailed comparisons of field variables at discreet points demonstrate the accuracy and robustness of the new SPH method. Copyright © 2014 John Wiley & Sons, Ltd.

The lid-driven cavity problem has been studied for four different Reynolds numbers up to 3200 employing an Incompressible SPH method. A new boundary condition treatment for solid walls was also tested in this problem. It yielded significant improvements over other SPH results of the same problem available in the literature. Moreover, close agreement with reference data has been obtained, hence demonstrating the potential capabilities and competitiveness of Incompressible SPH methods.

In this paper, we present a class of high-order accurate cell-centered arbitrary Lagrangian–Eulerian (ALE) one-step ADER weighted essentially non-oscillatory (WENO) finite volume schemes for the solution of nonlinear hyperbolic conservation laws on two-dimensional unstructured triangular meshes. High order of accuracy in space is achieved by a WENO reconstruction algorithm, while a local space–time Galerkin predictor allows the schemes to be high order accurate also in time by using an element-local weak formulation of the governing PDE on moving meshes. The mesh motion can be computed by choosing among three different node solvers, which are for the first time compared with each other in this article: the node velocity may be obtained either (i) as an arithmetic average among the states surrounding the node, as suggested by Cheng and Shu, or (ii) as a solution of multiple one-dimensional half-Riemann problems around a vertex, as suggested by Maire, or (iii) by solving approximately a multidimensional Riemann problem around each vertex of the mesh using the genuinely multidimensional Harten–Lax–van Leer Riemann solver recently proposed by Balsara *et al*. Once the vertex velocity and thus the new node location have been determined by the node solver, the local mesh motion is then constructed by *straight* edges connecting the vertex positions at the old time level *t*^{n} with the new ones at the next time level *t*^{n + 1}. If necessary, a rezoning step can be introduced here to overcome mesh tangling or highly deformed elements. The final ALE finite volume scheme is based directly on a space–time conservation formulation of the governing PDE system, which therefore makes an additional remapping stage unnecessary, as the ALE fluxes already properly take into account the rezoned geometry. In this sense, our scheme falls into the category of *direct* ALE methods. Furthermore, the geometric conservation law is satisfied by the scheme by construction.

We apply the high-order algorithm presented in this paper to the Euler equations of compressible gas dynamics as well as to the ideal classical and relativistic magnetohydrodynamic equations. We show numerical convergence results up to fifth order of accuracy in space and time together with some classical numerical test problems for each hyperbolic system under consideration. Copyright © 2014 John Wiley & Sons, Ltd.

A robust, better than second-order-accurate direct arbitrary Lagrangian-Eulerian WENO finite volume scheme with rezoning is presented for the equations of compressible gas dynamics and classical and relativistic magnetohydrodynamics (MHD and RMHD). Three different node solvers are compared with each other: (i) the method of Cheng and Shu, (ii) the node solver of Maire, and (iii) the genuinely multidimensional HLL Riemann solver of Balsara. The scheme is tested on difficult problems like the Gresho vortex or the RMHD blast wave problem.

The development of an adaptive free surface, mesh cutting, methodology, in order to analytically integrate pressures on varying wet parts of partially submerged surfaces in the presence of waves, is presented. Given a function of free-surface elevation, the algorithm checks for the intersection of the body with the free surface and, based on user-defined parameters, modifies the initial mesh, by subdividing the elements where necessary and eliminating others, via a quadtree approach. Redundant sub-divisions, generated in the quad-division process, are partially eliminated, but the quadrilateral nature of the elements is always kept. The free-surface function must be single-valued and its definition domain simply connected. Hydrostatic and Froude–Krylov forces are computed exactly on each panel by means of analytical formulations, which are derived and presented, based on the theory of linear gravity waves and from applying Green's theorem. Copyright © 2014 John Wiley & Sons, Ltd.

Analytic exact expressions for hydrostatic and Froude–Krylov forces and moments, on surfaces discretized by flat quadrilaterals, are formulated and presented for straightforward implementation in computer codes. The mesh is subjected to a quad subdivision adaptive process in way of the free surface, which may include waves—dry panels are eliminated. The adaptive scheme includes a secondary agglomeration step which—using a quadtree backlogging approach, together with geometric criteria—reduces the number of redundant panels created in the subdivision process.

We present a solver for a three-dimensional Poisson equation issued from the Navier–Stokes equations applied to model rivers, estuaries, and coastal flows. The three-dimensional physical domain is composed of an arbitrary domain in the horizontal direction and is bounded by an irregular free surface and bottom in the vertical direction. The equations are transformed vertically to the *σ*-coordinate system to obtain an accurate representation of top and bottom topographies. The method is based on a second-order finite volume technique on prisms consisting of triangular grids in the horizontal direction. The algorithm is accompanied by an analysis of different linear system solvers in order to achieve fast solutions. Numerical experiments are conducted to test the numerical accuracy and the computational efficiency of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.

This paper describes a new and efficient algorithm for solving a 3D Poisson equation based on a second-order finite volume technique and a *σ*-coordinate system. In addition, an analysis of different linear solvers is performed to obtain fast simulations.

This paper introduces tensorial calculus techniques in the framework of POD to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree *p*. Such nonlinear terms have an online complexity of , where *k* is the dimension of POD basis and therefore is independent of full space dimension. However, it is efficient only for quadratic nonlinear terms because for higher nonlinearities, POD model proves to be less time consuming once the POD basis dimension *k* is increased. Numerical experiments are carried out with a two-dimensional SWE test problem to compare the performance of tensorial POD, POD, and POD/discrete empirical interpolation method (DEIM). Numerical results show that tensorial POD decreases by 76× the computational cost of the online stage of POD model for configurations using more than 300,000 model variables. The tensorial POD SWE model was only 2 to 8× slower than the POD/DEIM SWE model but the implementation effort is considerably increased. Tensorial calculus was again employed to construct a new algorithm allowing POD/DEIM SWE model to compute its offline stage faster than POD and tensorial POD approaches. Copyright © 2014 John Wiley & Sons, Ltd.

This paper introduces tensorial calculus techniques in the framework of proper orthogonal decomposition (POD) to reduce the computational complexity of the reduced polynomial nonlinearities of any degree *p*. Such nonlinear terms have an online complexity of *O*(*k*^{p + 1}) - order of *k* at the power p+1, where *k* is the dimension of POD basis and therefore is independent of full space dimension. Reduced two-dimensional shallow water equation models based on tensorial POD, POD, and POD/discrete empirical interpolation method are developed and their performances are extensively analyzed.

In this paper, a high-order DG method coupled with a modified extended backward differentiation formulae (MEBDF) time integration scheme is proposed for the solution of unsteady compressible flows. The objective is to assess the performance and the potential of the temporal scheme and to investigate its advantages with respect to the second-order BDF. Furthermore, a strategy to adapt the time step and the order of the temporal scheme based on the local truncation error is considered. The proposed DG-MEBDF method has been evaluated for three unsteady test cases: (i) the convection of an inviscid isentropic vortex; (ii) the laminar flow around a cylinder; and (iii) the subsonic turbulent flow through a turbine cascade. Copyright © 2014 John Wiley & Sons, Ltd.

- A modified extended backward differentiation formulae (MEBDF) time integration scheme is here considered for the high-order discontinuous Galerkin solution of unsteady compressible flows.
- A deep investigation on the effect of Newton and GMRES tolerances on the performance of the temporal scheme is carried out.
- A strategy to adapt the order and time step of the temporal scheme during the computation is investigated in order to assess its benefits in the context of high-order discontinuous Galerkin method.

In this paper, we investigate the accuracy and efficiency of discontinuous Galerkin spectral method simulations of under-resolved transitional and turbulent flows at moderate Reynolds numbers, where the accurate prediction of closely coupled laminar regions, transition and developed turbulence presents a great challenge to large eddy simulation modelling. We take full advantage of the low numerical errors and associated superior scale resolving capabilities of high-order spectral methods by using high-order ansatz functions up to 12*t**h* order. We employ polynomial de-aliasing techniques to prevent instabilities arising from inexact quadrature of nonlinearities. Without the need for any additional filtering, explicit or implicit modelling, or artificial dissipation, our high-order schemes capture the turbulent flow at the considered Reynolds number range very well. Three classical large eddy simulation benchmark problems are considered: a circular cylinder flow at *R**e*_{D}=3900, a confined periodic hill flow at *R**e*_{h}=2800 and the transitional flow over a SD7003 airfoil at *R**e*_{c}=60,000. For all computations, the total number of degrees of freedom used for the discontinuous Galerkin spectral method simulations is chosen to be equal or considerably less than the reported data in literature. In all three cases, we achieve an equal or better match to direct numerical simulation results, compared with other schemes of lower order with explicitly or implicitly added subgrid scale models. Copyright © 2014 John Wiley & Sons, Ltd.

High-order discontinuous Galerkin spectral element schemes provide a method of simulating under-resolved turbulent and transitional flows at moderate Reynolds numbers accurately and efficiently, even without additional subgrid modelling. Using the same number of degrees of freedom, we show that these high-order formulations(up to *p* = 11) match or outperform lower order schemes with implicit or explicit large eddy simulation modelling strategies for three standard benchmark cases, while achieving highly competitive wall clock times.

This paper is concerned with the solution of heterogeneous problems by the interface control domain decomposition (ICDD) method, a strategy introduced for the solution of partial differential equations in computational domains partitioned into subdomains that overlap. After reformulating the original boundary value problem by introducing new additional control variables, the unknown traces of the solution at internal subdomain interfaces; the latter are determined by requiring that the (a priori) independent solutions in each subdomain undergo the minimization of a suitable cost functional.

We provide an abstract formulation for coupled heterogeneous problems and a general theorem of well-posedness for the associated ICDD problem. Then, we illustrate and validate an efficient algorithm based on the solution of the Schur-complement system restricted solely to the interface control variables by considering two kinds of heterogeneous boundary value problems: the coupling between pure advection and advection–diffusion equations and the coupling between Stokes and Darcy equations. In the latter case, we also compare the ICDD method with a classical approach based on the Beavers–Joseph–Saffman conditions. Copyright © 2014 John Wiley & Sons, Ltd.

Interface control domain decomposition (ICDD) methods are designed to solve PDEs in computational domains partitioned into overlapping subdomains and become especially attractive when applied to solve heterogeneous coupled problems where different kinds of PDE are set up in different subdomains. We provide an abstract formulation of coupled heterogeneous problems and a general theorem of well-posedness for the associated ICDD problem. We validate our method on two kinds of heterogeneous boundary value problems: the coupling between pure advection and advection–diffusion equations and the coupling between Stokes and Darcy equations.

This paper is the initial investigation into a new Lagrangian cell-centered hydrodynamic scheme that is motivated by the desire for an algorithm that resists mesh imprinting and has reduced complexity. Key attributes of the new approach include multidimensional construction, the use of flux-corrected transport (FCT) to achieve second order accuracy, automatic determination of the mesh motion through vertex fluxes, and vorticity control. Toward this end, vorticity preserving Lax–Wendroff (VPLW) type schemes for the two-dimensional acoustic equations were analyzed and then implemented in a FCT algorithm. Here, mesh imprinting takes the form of anisotropic dispersion relationships. If the stencil for the LW methods is limited to nine points, four free parameters exist. Two parameters were fixed by insisting that no spurious vorticity be created. Dispersion analysis was used to understand how the remaining two parameters could be chosen to increase isotropy. This led to new VPLW schemes that suffer less mesh imprinting than the rotated Richtmyer method. A multidimensional, vorticity preserving FCT implementation was then sought using the most promising VPLW scheme to address the problem of spurious extrema. A well-behaved first order scheme and a new flux limiter were devised in the process. The flux limiter is unique in that it acts on temporal changes and does not place *a priori* bounds on the solution. Numerical results have demonstrated that the vorticity preserving FCT scheme has comparable performance to an unsplit MUSCL-H algorithm at high Courant numbers but with reduced mesh imprinting and superior symmetry preservation. Copyright © 2014 John Wiley & Sons, Ltd.

In order to investigate a new paradigm for the construction of Lagrangian hydrocodes, members of the Lax–Wendroff family of schemes for the two-dimensional acoustic equations were analyzed. A vorticity preserving flux-corrected transport (VPFCT) scheme was built using the preferred first and second order methods and a vertex-centered temporal flux limiter. The VPFCT scheme was shown to have comparable phase and amplitude performance to an unsplit MUSCL-Hancock algorithm at large Courant numbers but with reduced mesh imprinting.

An algebraic variational multiscale-multigrid-multifractal method is proposed for large-eddy simulation of turbulent variable-density flow at low Mach number. In the multifractal subgrid-scale modeling approach, the subgrid-scale quantities are explicitly evaluated from a multifractal description of associated gradient fields. The multifractal subgrid-scale modeling approach is embedded into a residual-based form of the variational multiscale method. A particular feature of the proposed form of the multifractal subgrid-scale modeling approach is scale separation by level-transfer operators from plain aggregation algebraic multigrid methods to identify the required smaller resolved scales. In this study, we introduce a novel development of the multifractal subgrid-scale modeling approach for application to turbulent variable–density flow at low Mach number. Based on the physical background, we derive a variable-density extension of the multifractal subgrid-scale modeling approach to recover the subgrid-scale velocity and temperature field. The proposed method is validated via two numerical test cases. First, turbulent flow in a channel with a heated and a cooled wall is considered for two different temperature ratios. Second, turbulent flow over a backward-facing step with heating is investigated. The results obtained with the algebraic variational multiscale-multigrid-multifractal method are compared with results obtained with the widely-used dynamic Smagorinsky model and a residual-based variational multiscale method. Particularly, the results obtained for turbulent flow in a channel with a heated and a cooled wall indicate the excellent prediction quality achievable by the proposed method for turbulent variable-density flow at low Mach number. Copyright © 2014 John Wiley & Sons, Ltd.

Multifractal subgrid-scale modeling within a variational multiscale method is proposed for large-eddy simulation of turbulent variable–density flow at low Mach number. In the multifractal subgrid-scale modeling approach, the subgrid-scale velocity and temperature field are directly estimated from a multifractal description of their associate gradient fields. An excellent prediction quality is demonstrated for various numerical examples.

An immersed boundary method based on an FEM has been successfully combined with an elastic spring network model for simulating the dynamical behavior of a red blood cell (RBC) in Poiseuille flows. This elastic spring network preserves the biconcave shape of the RBC in the sense that after the removal of the body force for driving the Poiseuille flow, the RBC with its typical parachute shape in a tube does restore its biconcave resting shape. As a benchmark test, the relationship between the deformation index and the capillary number of the RBCs flowing through a narrow cylindrical tube has been validated. For the migration properties of a single cell in a slit Poiseuille flow, a slipper shape accompanied by a cell membrane tank-treading motion is obtained for Re , and the cell mass center is away from the center line of the channel due to its asymmetric slipper shape. For the lower Re ⩽0.0137, an RBC with almost undeformed biconcave shape has a tumbling motion. A transition from tumbling to tank-treading happens at the Reynolds number between 0.0137 and 0.03. In slit Poiseuille flow, the RBC can also exhibit a rolling motion like a wheel during the migration when the cell is released in the fluid flow with *φ* = *π*/2 and *θ* = *π*/2 (see Figure 12 for the definition of *φ* and *θ*). The lower the Reynolds number, the longer the rolling motion lasts; but the equilibrium shape and position are independent from the cell initial position in the channel. Copyright © 2014 John Wiley & Sons, Ltd.

An immersed boundary method with the elastic spring model has been successfully combined and validated with finite element and operator splitting methods for simulating red blood cell (RBC) motion in three-dimensional Poiseuille flow. RBC can tumble as in shear flow at low Reynolds numbers. RBC can roll like a wheel in slit Poiseuille flow during the migration toward the central region with a specified initial orientation. The lower the Reynolds number, the longer the rolling motion lasts.

The finite volume method with exact two-phase Riemann problems (FIVER) is a two-faceted computational method for compressible multi-material (fluid–fluid, fluid–structure, and multi-fluid–structure) problems characterized by large density jumps, and/or highly nonlinear structural motions and deformations. For compressible multi-phase flow problems, FIVER is a Godunov-type discretization scheme characterized by the construction and solution at the material interfaces of local, exact, two-phase Riemann problems. For compressible fluid–structure interaction (FSI) problems, it is an embedded boundary method for computational fluid dynamics (CFD) capable of handling large structural deformations and topological changes. Originally developed for inviscid multi-material computations on nonbody-fitted structured and unstructured grids, FIVER is extended in this paper to laminar and turbulent viscous flow and FSI problems. To this effect, it is equipped with carefully designed extrapolation schemes for populating the ghost fluid values needed for the construction, in the vicinity of the fluid–structure interface, of second-order spatial approximations of the viscous fluxes and source terms associated with Reynolds averaged Navier–Stokes (RANS)-based turbulence models and large eddy simulation (LES). Two support algorithms, which pertain to the application of any embedded boundary method for CFD to the robust, accurate, and fast solution of FSI problems, are also presented in this paper. The first one focuses on the fast computation of the time-dependent distance to the wall because it is required by many RANS-based turbulence models. The second algorithm addresses the robust and accurate computation of the flow-induced forces and moments on embedded discrete surfaces, and their finite element representations when these surfaces are flexible. Equipped with these two auxiliary algorithms, the extension of FIVER to viscous flow and FSI problems is first verified with the LES of a turbulent flow past an immobile prolate spheroid, and the computation of a series of unsteady laminar flows past two counter-rotating cylinders. Then, its potential for the solution of complex, turbulent, and flexible FSI problems is also demonstrated with the simulation, using the Spalart–Allmaras turbulence model, of the vertical tail buffeting of an F/A-18 aircraft configuration and the comparison of the obtained numerical results with flight test data. Copyright © 2014 John Wiley & Sons, Ltd.

The embedded boundary method FIVER for compressible fluid and fluid–structure interaction (FSI) problems is extended to laminar and turbulent viscous flows. Two support algorithms are also presented. The first one focuses on the fast computation of the time-dependent distance to the wall. The second algorithm addresses the robust computation of the flow-induced loads on embedded surfaces. FIVER's potential for turbulent FSI problems is also demonstrated with the simulation of the vertical tail buffeting of an F/A-18 aircraft configuration.

This paper reports on the application and development of a fully hyperbolic and fully conservative two-phase flow model for the simulation of gas and magma flow within volcanic processes. The model solves a set of mixture conservation equations for the gas and magma two-phase flow with velocity non-equilibrium. In this model, the effect of the relative velocity is introduced by a kinetic constitutive equation with other equations for volume and mass fractions of the gas phase. The model is examined numerically by the widely used finite volume Godunov methods of centered-type. Using the Riemann problem, we numerically simulate wave propagation and the development of shocks and rarefactions in volcanic eruptions. These simulations are of magma fragmentation type where the relative velocity continues to dominate. A series of test cases whose solution contains features relevant to gas–magma mixtures are conducted. In particular, numerical results indicate that the model implementation predicts key features of the relative velocity within volcanic processes without any mathematical or physical simplifications. Simulation results are sharply and accurately provided without any spurious oscillations in all of the flow variables. The numerical methods and results are also compared with other numerical methods available in the literature. It is found that the provided resolutions are more accurate for the considered test cases. Copyright © 2014 John Wiley & Sons, Ltd.

This study introduces a well-defined mathematical model for the relative velocity investigation of two-phase flows within volcanic processes. The model is used to examine the relative velocity wave propagation and the development of shocks and rarefactions structure within such processes. Well-developed finite volume methods are applied to solve the governing equations. Numerical simulation of non-equilibrium phenomena between phases has been conducted and validated. Results show that the model is beneficial for the study of velocity non-equilibrium of volcanic processes.

In this study, a hybridizable discontinuous Galerkin method is presented for solving the incompressible Navier–Stokes equation. In our formulation, the convective part is linearized using a Picard iteration, for which there exists a necessary criterion for convergence. We show that our novel hybridized implementation can be used as an alternative method for solving a range of problems in the field of incompressible fluid dynamics. We demonstrate this by comparing the performance of our method with standard finite volume solvers, specifically the well-established finite volume method of second order in space, such as the icoFoam and simpleFoam of the OpenFOAM package for three typical fluid problems. These are the Taylor–Green vortex, the 180-degree fence case and the DFG benchmark. Our careful comparison yields convincing evidence for the use of hybridizable discontinuous Galerkin method as a competitive alternative because of their high accuracy and better stability properties. Copyright © 2014 John Wiley & Sons, Ltd.

A numerical comparison of a hybridizable discontinuous Galerkin method and a finite volume method is given. The hybridizable discontinuous Galerkin method has been reformulated as Picard iteration and hybridized. The methods are introduced, and four numerical standard simulations are used in order to benchmark and evaluate the solver – the Taylor–Green vortex, the fence case and the 2D DFG benchmark. The benchmarks suggest that hybridized discontinuous Galerkin methods are a viable alternative to finite volume solvers for incompressible fluid simulations.

Transpiration cooling using ceramic matrix composite materials is an innovative concept for cooling rocket thrust chambers. The coolant (air) is driven through the porous material by a pressure difference between the coolant reservoir and the turbulent hot gas flow. The effectiveness of such cooling strategies relies on a proper choice of the involved process parameters such as injection pressure, blowing ratios, and material structure parameters, to name only a few. In view of the limited experimental access to the subtle processes occurring at the interface between hot gas flow and porous medium, reliable and accurate simulations become an increasingly important design tool. In order to facilitate such numerical simulations for a carbon/carbon material mounted in the side wall of a hot gas channel that are able to capture a spatially varying interplay between the hot gas flow and the coolant at the interface, we formulate a model for the porous medium flow of Darcy–Forchheimer type. A finite-element solver for the corresponding porous medium flow is presented and coupled with a finite-volume solver for the compressible Reynolds-averaged Navier–Stokes equations. The two-dimensional and three-dimensional results at Mach number *M**a* = 0.5 and hot gas temperature *T*_{HG}=540 K for different blowing ratios are compared with experimental data. Copyright © 2014 John Wiley & Sons, Ltd.

Transpiration cooling using ceramic matrix composite materials is an innovative concept for cooling rocket thrust chambers. To investigate the interaction between the cooling gas and the hot gas, the Darcy–Forchheimer equations assuming thermal non-equilibrium and the compressible Reynolds-averaged Navier–Stokes equations are coupled. Suitable coupling conditions are developed and tested by means of two-dimensional and three-dimensional simulations, which are compared with experimental data.

A model for multidimensional compressible two-phase flow with pressure and velocity relaxations based on the theory of thermodynamically compatible system is extended to study liquid–gas flows with cavitation. The model assumes for each phase its own pressure and velocity, while a common temperature is considered. The governing equations form a hyperbolic system in conservative form and are derived through the theory of a thermodynamically compatible system. The phase pressure-equalizing process and the interfacial friction are taken into account in the balance laws for the volume fractions of one phase and for the relative velocity by adding two relaxation source terms, while the phase transition is introduced into the model considering in the balance equation for the mass of one phase the relaxation of the Gibbs free energies of the two phases. A modification of the central finite-volume Kurganov–Noelle–Petrova method is adopted in this work to solve the homogeneous hyperbolic part, while the relaxation source terms are treated implicitly. In order to investigate the effect of the mass transfer in the solution, a 1D cavitation tube problem is presented. In addition, two 2D numerical simulations regarding cavitation problem are also studied: a cavitating Richtmyer–Meshkov instability and a laser-induced cavitation problem. Copyright © 2014 John Wiley & Sons, Ltd.

A model for multidimensional compressible two-phase flow with pressure and velocity relaxations, based on the theory of thermodynamically compatible system (Romenski *et al*. 2010) is extended to study liquid–gas flows with cavitation. The phase transition is modeled in the balance equation for the mass of one phase through the relaxation of the Gibbs free energies of the two phases. A 1D cavitation tube problem and two 2D numerical simulations regarding cavitation problem are studied: a cavitating Richtmyer–Meshkov instability and a laser-induced cavitation problem.

Nonlinear aerodynamics of wings may be evaluated using an iterative decambering approach. In this approach, the effect of flow separation due to stall at any wing section is modeled as an effective reduction in section camber. The approach uses a wing analysis method for potential-flow calculations and viscous airfoil lift curves for the sections as input. The calculation procedure is implemented using a Newton–Raphson iteration to simultaneously satisfy the boundary condition, which comes from potential-flow wing theory, and drive the sectional operating points toward their respective viscous lift curves, as required for convergence. Of particular interest in this research is the calculation of the residuals during the Newton iteration. Unlike a typical implementation of the Newton iteration, the residual calculation is not performed via a straightforward function evaluation, but rather by estimating the target operating points on the input viscous lift curves. Estimation of these target operating points depends on the assumptions made in the cross-coupling of the decambering at the different sections. This paper presents four residual calculation schemes for the decambering approach. The residual calculation schemes are compared against each other to assess computational speed and robustness. Decambering results are also compared with higher-order computational fluid dynamics (CFD) solutions for rectangular and swept wings. Results from the best scheme compare well with the CFD solutions for the rectangular wing, motivating further development of the method. Poor predictions for the swept wings are traced to spanwise propagation of separated flow at stall, highlighting the limitations of the current approach. Copyright © 2014 John Wiley & Sons, Ltd.

An iterative approach is presented for rapid post-stall aerodynamic prediction of wings for use in flight simulation and design. This approach uses an analysis method for potential flow calculations and viscous airfoil data as input. A Newton–Raphson iteration is implemented to simultaneously satisfy the boundary condition, from potential flow, and drive the sectional operating points toward their respective input curves, for convergence. Four residual calculation schemes are presented, and results from the best scheme compare favorably against CFD results.

This paper focuses on the fluid boundary separation problem of the conventional dynamic solid boundary treatment (DSBT) and proposes a modified DSBT (MDSBT). Classic 2D free dam break flows and 3D dam break flows against a rectangular box are used to assess the performance of this MDSBT in free surface flow and violent fluid–structure interaction, respectively. Another test, water column oscillations in a U-tube, is specially designed to reveal the applicability of dealing with two types of particular boundaries: the wet–dry solid boundary and the large-curvature solid boundary. A comparison between the numerical results and the experimental data shows that the MDSBT is capable of eliminating the fluid boundary separation, improving the accuracy of the solid boundary pressure calculations and preventing the unphysical penetration of fluid particles. Using a 2D SPH numerical wave tank with MDSBT, the interactions between regular waves and a simplified vertical wave barrier are simulated. The numerical results reveal that the maximum horizontal force occurs at the endpoint of the vertical board, and with the enlargement of the relative submerged board length, the maximum moment grows linearly; furthermore, the relative average mass transportation under the breakwater initially increases to 11.14 per wave strike but is later reduced. The numerical simulation of a full-scale 3D wave barrier with two vertical boards shows that the wave and structure interactions in the practical project are far more complicated than in the simplified 2D models. The SPH model using the MDSBT is capable of providing a reference for engineering designs. Copyright © 2014 John Wiley & Sons, Ltd.

This paper proposes a modified dynamic solid boundary treatment for SPH method and validates the new model with water column oscillations in a U-tube. The interactions between regular waves and a 2D simplified vertical wave barrier are simulated with varying relative submerged board lengths, and detailed force analysis is conducted on the structures. A demonstrative test case involving a 3D wave barrier is also provided.

We propose and analyze an algorithm for the robust construction of curved meshes in two and three dimensions. The meshes are made of curved simplexes. The algorithm starts from a mesh made of straight simplexes, and using a linear elasticity analogy applied on well-chosen data, one can generate a curved mesh. Note that if the initial mesh has a boundary layer, this method allows to conserve it on the final mesh. This algorithm is used on several airfoils in two and three dimensions, including a turbulent M6 wing. Copyright © 2014 John Wiley & Sons, Ltd.

Starting from an initial straight mesh and using a linear elasticity analogy written on Bezier control points, we provide an algorithm that ‘bends’ the mesh and respects the boundary layer structure. Examples are given in two and three dimensions.