International Journal for Numerical Methods in Fluids

Reduced order models of continuous high order systems are usually produced in the discrete time domain for a fixed time step. When using an ROM as a surrogate for the high order system for continuation, an equivalent continuous ROM that can be used for any time step is required. A discrete ROM may work for the time step used in construction, but leads to an unstable continuous ROM. This problem is overcome by the restarting approach presented in this study.

A computational method to study filtration properties of porous filters is proposed. On an example of 3D structured porous media with staggered and in line arrangement of square rods, we show the influence of the inner structure on the filtration characteristics. In both geometries, filtration depends strongly on the particle inertia and the microstructure of the porous medium. The observed dependencies give insight in the design parameters for effective controlled separation of particles by porous filters.

This paper presents the implementation of an all-Mach scheme in the implicit CFD solver of Liverpool. The scheme was presented by F. Rieper in 2011, and it has so far been used with explicit schemes. The paper details the development of an analytical, approximate Jacobian for the implicit CFD solver employed. The Jacobian resulted in efficient computations of low Mach number flows ranging from aerofoils to a wind turbine blade. The following figure presents the obtained wake of the wind turbine blade in comparisons with experimental measurements obtained during the MEXICO research project. The implicit solver, combined with the all-Mach scheme is suitable for the analysis of low and high-speed flows without the need for numerical tuning of the solver's parameters and with good efficiency in convergence.

The χ —scheme is used with high resolution convection schemes to ensure that the sum of chemical species mass fractions add to one. We show that this scheme degrades to a diffusive first order when a chemical species vanishes from the mixture, and we propose a remedy to this problem. Also, a computationally efficient alternative scheme is proposed that shows improvements in the accuracy and the computational time.

Sixth-order monotonicity-preserving optimized scheme (OMP6) for the numerical solution of conservation laws is developed on the basis of the dispersion and dissipation optimization and monotonicity-preserving technique. The nonlinear spectral analysis method is developed and is used for the purpose of minimizing the dispersion errors and controlling the dissipation errors. Test cases show that the new scheme has robust shock capturing capability and high resolution for the small-scale waves due to fewer numerical dispersion and dissipation errors. Moreover, the new scheme has higher computational efficiency than the well-used WENO schemes.

In this paper, a semi-implicit numerical model for one-dimensional urban drainage networks is formulated in such a fashion as to intrinsically account for arbitrary cross sections, for the occurrence of dry areas, for free surface, and for pressurized flows. The governing differential equations are discretized with a consistent mass conservative scheme that naturally applies to all flow regimes. The resulting mildly nonlinear system, at every time step, is efficiently solved with a converging, properly devised, nested Newton-type algorithm. It will be shown that with the proposed semi-implicit model, high accuracy can be achieved at a moderate computational cost.

Performance of fourth-order solution to shallow water equations by Finite Volume Method with Shock Capturing Schemes has been shown on a compound channel with and without a bridge. The numerical results quite agreed with the experimental ones.

A system of weighted averaged Reynolds equations was developed, and an indirect scheme was proposed to address the essential details of vertical distributions of horizontal velocity for one-dimensional steady open-channel flow. The weighted averaged velocities were solved through the weighed averaged equations; then the velocity profile variables were solved through the expansion equations of the weighted averaged velocities.

A quasi-conservative interface-capturing method based on mass fraction is developed to solve the Riemann problem in a multi-component compressible flow. The method is simple and relaxed; it can be extended to m-component fluid mixture by using only m + 4 equations. Numerical examples show that the mass fraction model performs well in the multi-component Riemann problem with very different EOSs and extreme initial conditions.

We develop an efficient and accurate numerical method for the solution of the non-stationary compressible Navier–Stokes equations. We derive residual error estimates that are able to identify the spatial, temporal and algebraic errors and therefore and moreover we define an algorithm, which is able to balance these errors. The figure showing a viscous shock–vortex interaction demonstrate the applicability of the method.

In this paper, we extend the Multidimensional Optimal Order Detection (MOOD) method, both the convection equation, and the Euler system to 3D mixed meshes and simplify the u2 detection process previously developed. The optimal high order of accuracy is numerically assessed on smooth solutions, whereas spurious oscillations near singularities are prevented. Finally, the intrinsic positivity-preserving property of the MOOD method is confirmed in 3D, and we provide computational cost estimates that supports the MOOD method competitiveness.

We attempt to improve accuracy in the high-wavenumber region in direct numerical simulation of incompressible wall turbulence by improving accuracy of viscous terms in the Navier-Stokes equations. Increase in required computational cost will not be crucial because this improvement does not increase computational cost for solving the Poisson equation. The results show that accuracy improvement of the viscous terms improves accuracy of higher-order statistics and various spectra in the high-wavenumber region.

To predict the bed load transport induced by dam break waves over a mobile bed, the proposed two-dimensional two-layer shallow water description considers an upper layer made of clear water and a lower layer made of a dense mixture of water and moving grains. The system of governing equations, written so that the conservative part is hyperbolic, is solved by an HLL finite volume scheme on an unstructured triangular mesh. The numerical model is tested against laboratory experiments of waves expanding over sand beds in an abrupt enlargement and over a floodplain.

Detailed validation of a newly developed very LES model is presented for the turbulent separated flows such as the flow past a square cylinder, circular cylinder, and a backward-facing step at different Reynolds number. The model was found to be able to produce quite satisfactory results on quite coarse mesh compared with conventional LES. The model has considerable potential in the predictions of complex turbulent high-Reynolds-number flow in engineering applications.

In this paper, we describe a dimension split method (DSM) for the three-dimensional steady incompressible Navier–Stokes equations. The basic idea of DSM is that three-dimensional space is split up into a cluster of two-dimensional manifolds and then the three-dimensional solution is approximated by the solutions on these two-dimensional manifolds. Because of split property of DSM, all computation is carried out on these two-dimensional manifolds, which greatly reduces the difficulty in the mesh generation; moreover, these two-dimensional problems can be computed simultaneously.

A data compression method based on image encoding techniques is presented and applied to the flow simulation data sets, including flow around a Formula 1 racing car with O( 10⁸) mesh points. Visualization of flow field indicates compressed data reproduce velocity distribution well, compared with the original data. The data size after the compression is only 3.68% of the original data, showing good performance of the present method in terms of compressed data quality and data compression ratio.

This paper presents a hierarchical application of VMS ideas for deriving residual-based turbulence models for problems with moving boundaries and interfaces. An overlapping additive decomposition of velocity and pressure fields into coarse and fine scale components leads to coarse and fine scale mixed-field problems. A bubble functions based approach is employed to consistently derive fine-scale models, which results in a residual-based turbulence modeling method that is free of any embedded or tunable parameters.

We compare simulations of Taylor flow, that is, pressure-driven flow of elongated, bullet-shaped bubbles in a narrow channel. Four different codes based on two different mathematical models are compared against each other and to experimental data obtained by X-ray tomography. Despite the differences in modeling, good agreement is demonstrated in all instances.

An application of the finite point method to compressible flow problems involving moving or deformable boundaries is presented in this work. The methodology proposed combines meshless adaptivity with a typical domain deformation technique in a cost effective way. Typical moving/deformable boundary problems and a fluid structure interaction analysis involving static aeroelasticity are provided. The results show the potential of the meshless technique to solve practical problems in engineering.

We present a numerical investigation for the collapse and rebound of a laser-induced cavitation bubble in liquid water. The compressibility of the liquid and vapor is involved. In addition, great focus is devoted to study the effects of phase transition and the existence of a noncondensable gas on the dynamics of the collapsing bubble. We compare our results with experimental ones. Also our results confirm some expected physical phenomena.

In this paper, (i) a new semi-discrete central scheme for a scalar conservation law, which allows for spatial variability of the storage coefficient, is developed; (ii) the application of the new scheme to two-phase flow in strongly heterogeneous porous media is discussed; and (iii) comparisons with the uncorrelated porosity/permeability case and homogeneous porosity with linear and nonlinear flux functions are presented.

The physical space version of the stretched vortex subgrid scale model is tested in LES of the turbulent lid-driven cubic cavity flow by using higher order finite-difference methods. The effects of different vortex orientation models and subgrid turbulence spectrums are assessed.

In this paper, a combined DF/FD–level set method has been provided for two-phase flows interacting with moving bodies on fixed Cartesian grids. Water entry problems are performed to validate the present combined DF/FD–level set method for two phase flows with moving bodies with various shapes. The vorticity contours and the vertical force acting on the cylinder have been compared with results of other researches, and an excellent agreement has been obtained.

An example of low-complexity robust shape optimization using optimal sampling of the functioning parameter range, incomplete sensitivity and target-based weighting.

We propose a well-balanced stable generalized Riemann problem scheme for the shallow water equations with irregular bottom topography based on moving triangular meshes. Numerical tests show the accuracy, efficiency and robust of the scheme. In order to stabilize the computations near equilibria, we use the Rankine-Hugoniot condition to remove a singularity from the GRP solver. We develop a remapping onto the new mesh (after grid movement) based on equilibrium variables. This, together with already established techniques, guarantees the well-balancing. Numerical tests show the accuracy, efficiency, and robustness of the GRP moving mesh method: lake at rest solutions are preserved even when the underlying mesh is moving (e.g., mesh point are moved to regions of steep gradients) and various comparisons with fixed coarse and fine meshes demonstrate high resolution at relatively low cost.

We proposed a well-balanced 2D shallow water model to solve flow over complex topography. A Homogenous Flux Method was used to treat the bed slope term as a flux to be incorporated into the flux gradient to maintain the balance. The model was solved by the second-order total-variation-diminishing version of the weighted average flux/Harten-Lax-van Leer-Contract and tested by a series of benchmark cases. Finally, it was applied to a large-scale real-world flood over an irregular topography to demonstrate the technique's capability.

We propose a new boundary condition for the pressure Poisson equation after replacing the incompressibility constraint by the pressure Poisson equation. Hence, we obtain the numerical scheme to solve the incompressible Navier–Stokes equations with open boundary condition. The new scheme can obtain high-order accuracy.

A description of a finite-volume code for the simulation of transient compressible flows is given. The verification and validation of this code for use in hypersonics applications is demonstrated with a detailed set of case studies. An important lesson is provided about the utility of experimental data for validation of hypersonic flow solvers.

This work describes a nonlinear, three-dimensional spectral collocation method for the simulation of the incompressible Navier–Stokes equations under the Boussinesq approximation. This model implements bottom topography via coordinate mapping, and it permits simulation of boundary-layer dynamics in environmental and geophysical flows. A geometric-multigrid based finite-difference preconditioner is used to ensure performance on parallel systems, giving resolution-independent convergence rates.

A new subgrid closure model for two-material cells is proposed. The conservative quantities of the entire cell are apportioned between two materials, and then, pressure and velocity are fully or partially equilibrated by modeling subgrid wave interactions. The generality, robustness, and efficiency of the model make it useful in principle in algorithms, such as ALE methods, volume of fluid methods, and even some mixture models, for compressible two-phase flow computations.

This paper reports on the comparative study of various radiation type non-reflective outflow boundary conditions and of the standard boundary condition where the Neumann condition with zero normal derivative is applied for the simulation of a turbulent plume flow. The results showed a one-dimensional scheme in which advection and diffusion terms are included in the radiation equation as the optimum approach for the plume simulation.

This paper presents noniterative interface reconstruction algorithms. The noniterative algorithms are very fast, and with the piecewise linear algorithms, it was possible to reconstruct volume of fluid within the machine tolerance. The quadratic algorithm gives a more accurate estimate of the length of the interface.

In this paper, we propose a time integrator coupling strategy that can be used to couple finite volume and finite element subdomains. This method relies on the use of the appropriate compatibility relation of the fluid equations. By ensuring the zero interface energy condition, we can preserve the minimum order of accuracy in time as well as the stability.

Our goal is to study the transient heat load within solid structures of complex geometries via a fluid-structure coupling. This coupling is challenging because of the great disparities in time scales of the physical models. In the quasi-dynamic procedure proposed in the paper, a solid transient state is coupled with a sequence of fluid steady states. A numerical application simulating the severe thermal conditions of a solid propellant rocket has shown that the CPU time is greatly reduced, while maintaining a very good accuracy.

Eight-degree polynomial upwind scheme (EPUS) is an alternative upwind scheme for stable computation of fluid dynamics algorithms. It is a three-point stencil for numerical flux reconstruction of class C2 and formulated by employing the convection boundedness criterion and total variation diminishing stability criteria. The advantage of the EPUS scheme is that it adopts a free parameter that can be used to control dissipation and dispersion. The EPUS scheme is simple implement in existent codes, transports scalars maintaining nonoscillatory profiles, and provides accurate solutions to complex fluid flows.

A p-adaptive hybridizable discontinuous Galerkin method based on error estimation is proposed for the solution of scattering problems (Helmholtz for nonconstant coefficients in unbounded domains). This approach outperforms high-order continuous Galerkin. The figure shows the final distribution of the approximation order p for the desired accuracy in a challenging engineering problem: wave propagation in Barcelona's harbor.

The comparison of error and work estimates shows that even for relative accuracy in the 0.1% range, which is one order below the typical accuracy of engineering interest (1% range), linear elements may outperform all higher-order elements. As expected, the estimates also show that the optimal order of elements in terms of work and storage demands depends on the desired relative accuracy. The comparison of work estimates for high-order elements and their finite difference counterparts reveals a work-ratio of several orders of magnitude. It thus becomes questionable if general geometric flexibility via micro-unstructured grids is worth such a high cost.

A verification and validation procedure for yacht sail aerodynamics is presented. Guidelines and an example of application are provided. The importance of verification and validation to assess modelling error and ranking different deign candidates is discussed. In the presented example, lift, drag and L2 norm of the pressures were computed with uncertainties of the order of 1% with a number of cells of the order of one million.

Kidder's isentropic compression problem. Comparison of the analytical result (solid line) with the numerical results computed by the scheme of Maire et al. and by the current entropy fixed scheme for the density at t = 0.99 with a grid n_x = 25, n_y = 44.

A numerical study is presented of a universal method for interpolating solution data across discontinuous mesh interfaces. The method utilises radial basis functions for n-dimensional volume interpolation. It is shown that high spatial order data transmission is achievable for a modest computational overhead.

In the following paper, we propose a brand new method for solving the magnetohydrodynamic (MHD) equations. This is a first time presentation of the Inclusion of Advection Upstream Splitting Method-MHD fluxes for solving the ideal MHD equations with a PISO type algorithm. A detailed validation is presented using canonical test cases to prove the claimed findings.

In this work, we present an explicit formulation for reduced-order models of the stabilized finite element approximation of the incompressible Navier–Stokes equations. The main advantage of this explicit treatment is that it allows for the easy use of hyper-reduced-order models, because only a single vector needs to be recovered by means of a gappy data reconstruction procedure. Numerical examples compare the reduced-order model results with the full-order model velocity and pressure fields.

Unstructured grids in hydrodynamic simulations offer great flexibility but exhibit numerical diffusion, which is dependent on orientation of the cells relative to the flow. Analytical descriptions of this relationship are found for a finite-volume scheme implementing scalar transport on regular triangular grids. An unsupervised method for generating grids locally aligned with the dominant flow is presented and shown to significantly decrease across-flow grid diffusion.

A general procedure has been developed for the simulation of charged liquid and electrostatically atomized sprays. The procedure was validated through simulations of previously published charged spray experiments. Results successfully showed that the general spatial characteristics and dynamics of a charged liquid spray can be reproduced, including the axial and radial dispersal patterns of droplets and the distribution of mean droplet diameters throughout the spray plume.

Implementation or partial-element wetting and drying in 1D ADCIRC results in improved wetting front propagation and mass balance compared with the previous algorithm, which treats entire elements as either wet or dry. Partial-element wetting and drying is achieved by applying a scaling factor to the primitive continuity prior to formulation of the generalized wave continuity equation.

The four cell-based agglomerated coarse grids for NACA0012 airfoil by the present method and MGridGen are shown. Top four is generated by the present method and the bottom is generated by the open library MGridGen.