International Journal for Numerical Methods in Fluids

Cover image for Vol. 83 Issue 7

Early View (Online Version of Record published before inclusion in an issue)

Edited By: Charbel Farhat, Wolfgang A. Wall

Impact Factor: 1.447

ISI Journal Citation Reports © Ranking: 2015: 17/30 (Physics Fluids & Plasmas); 41/101 (Mathematics Interdisciplinary Applications); 56/104 (Computer Science Interdisciplinary Applications); 62/135 (Mechanics)

Online ISSN: 1097-0363

Associated Title(s): International Journal for Numerical Methods in Biomedical Engineering, International Journal for Numerical Methods in Engineering, International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Numerical Linear Algebra with Applications


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  1. Research Articles

    1. A coupled continuous and discontinuous finite element method for the incompressible flows

      Puyang Gao, Jie Ouyang, Pengfei Dai and Wen Zhou

      Version of Record online: 19 JAN 2017 | DOI: 10.1002/fld.4358

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      This paper develops a coupled continuous and discontinuous Galerkin method based on the split scheme to solve the Navier–Stokes equations. This coupled method can simulate incompressible flow efficiently and accurately.

  2. Short Communication

    1. SPH simulation of oblique shocks in compressible flows

      Matti Silla and Volfango Bertola

      Version of Record online: 22 DEC 2016 | DOI: 10.1002/fld.4356

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      The fully Lagrangian mesh-free smoothed particle hydrodynamic method is used to simulate oblique shocks in a compression corner.

      A novel method to generate ghost particles is proposed to treat the corner boundary condition.

      The method predicts values of the shock angle in very good agreement with the analytical solution.

  3. Research Articles

    1. An efficient front-tracking method for simulation of multi-density bubbles

      M. T. Mehrabani, M. R. H. Nobari and G. Tryggvason

      Version of Record online: 21 DEC 2016 | DOI: 10.1002/fld.4355

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      Schematic comparison of the masked bubble strategy versus full-domain strategy in front-tracking method in a curved duct.

    2. A moving particle semi-implicit method for free surface flow: Improvement in inter-particle force stabilization and consistency restoring

      Hao Xiang and Bin Chen

      Version of Record online: 21 DEC 2016 | DOI: 10.1002/fld.4354

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      IFS-CR-MPS method was proposed to suppress the compressive instability of MPS method. For inter-particle force stabilization, a hyperbolic-shaped quintic kernel function was developed with a non-negative second order derivative. The first order derivative of the said function was adopted to express the contribution of neighbor particles to prevent violent repulsive inter-particle force. For consistency restoring, the Taylor series expansion and hyperbolic-shaped kernel were combined to achieve C1 consistency for gradient approximation to improve the accuracy of viscosity and pressure calculation.

    3. You have full text access to this OnlineOpen article
      Improving the convergence behaviour of a fixed-point-iteration solver for multiphase flow in porous media

      P. Salinas, D. Pavlidis, Z. Xie, A. Adam, C. C. Pain and M. D. Jackson

      Version of Record online: 18 DEC 2016 | DOI: 10.1002/fld.4357

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      Improving the convergence behaviour of a fixed-point-iteration solver for multiphase flow in porous media: Development of a more robust non-linear solver with increase effective convergence rate to admit large Courant numbers in multiphase flow in porous media by adding strengthening the coupling between velocity and saturation, adding vanishing artificial diffusion and calculating an efficient backtracking parameter.

    4. Monotone nonlinear finite-volume method for nonisothermal two-phase two-component flow in porous media

      Martin Schneider, Bernd Flemisch and Rainer Helmig

      Version of Record online: 12 DEC 2016 | DOI: 10.1002/fld.4352

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      We present a new monotone nonlinear finite-volume scheme for the nonisothermal two-phase two-component flow equations in porous media. The behavior of this scheme is analyzed, and the condition numbers of occurring matrices are compared with linear finite-volume schemes. Additionally, the convergence behavior of iterative solvers is investigated, and it is shown that the nonlinear scheme is more efficient than its linear counterpart.

    5. Interface-preserving level-set reinitialization for DG-FEM

      Thomas Utz, Florian Kummer and Martin Oberlack

      Version of Record online: 9 DEC 2016 | DOI: 10.1002/fld.4344

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      In contrast to common techniques, our method relies on solving a nonlinear elliptic PDE iteratively. This leads to improved stability, especially when dealing with interface geometries with high curvature compared to the element size.

    6. You have full text access to this OnlineOpen article
      Application of central differencing and low-dissipation weights in a weighted compact nonlinear scheme

      Tomohiro Kamiya, Makoto Asahara and Taku Nonomura

      Version of Record online: 9 DEC 2016 | DOI: 10.1002/fld.4343

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      This paper proposes WCNS-CU-Z, which is a high-resolution scheme, because interpolation of this scheme employs a central stencil constructed by upwind and downwind stencils. Moreover, we adapt low-dissipative weights to this scheme in order to converge sufficient accuracy in the smooth region. The figure indicates that density distribution of double Mach problem which one of the general shock wave problems. The sixth-order WCNS-CU-Z show reasonably good shock-capturing properties and low dissipation compared with fifth-order weighted compact nonlinear scheme (WCNS) and also the seventh-order WCNS.

    7. MLPG_R method for modelling 2D flows of two immiscible fluids

      Yan Zhou, Q. W. Ma and S. Yan

      Version of Record online: 9 DEC 2016 | DOI: 10.1002/fld.4353

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      A two-phase flow model based on MLPG_R method is proposed by forming a pressure equation for the interface particles considering the continuous pressure and the discontinuous specific pressure gradient at the interface. With a new method, second-order convergent rate for layered sloshing with various density ratios and filling ratios can be achieved as shown below.

    8. Numerical analysis of conservative unstructured discretisations for low Mach flows

      J. Ventosa-Molina, J. Chiva, O. Lehmkuhl, J. Muela, C. D. Pérez-Segarra and A. Oliva

      Version of Record online: 1 DEC 2016 | DOI: 10.1002/fld.4350

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      In the paper finite-volume collocated and unstructured discretizations to simulate Low Mach flows are analyzed. The collocated method is shown to be more computationally efficient. Furthermore, a Symmetry-Preserving and Upwinding numerical schemes for face interpolations are studied, focusing on their behavior on unstructured meshes. Tests cases include non-reactive and chemically reactive simulations.

    9. Role of the momentum interpolation mechanism of the Roe scheme in shock instability

      Xiao-dong Ren, Chun-wei Gu and Xue-song Li

      Version of Record online: 29 NOV 2016 | DOI: 10.1002/fld.4351

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      1. The inherent momentum interpolation method (MIM) of the Roe scheme plays the most important role in the shock instability phenomenon.
      2. Unexpected MIM is activated on the cell faces nearly parallel to high-Mach-number flows and low-Mach-number cells in numerical shock.
      3. An improved Roe scheme is proposed, which consider the requirement of MIM for incompressible and compressible flows, and can achieve the aim of decreasing numerical dissipation to cure shock instability.
    10. An ALE approach to mechano-chemical processes in fluid–structure interactions

      Yifan Yang, Thomas Richter, Willi Jäger and Maria Neuss-Radu

      Version of Record online: 16 NOV 2016 | DOI: 10.1002/fld.4345

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      In this paper, we formulate a mechano-chemical fluid–structure interaction problem. A plaque formation model is chosen as a proof of concept scenario. The ALE method is chosen to solve the system numerically and delivers very reliable results.

    11. A new mesh relaxation approach and automatic time-step control method for boundary integral simulations of a viscous drop

      I. R. Siqueira, R. B. Rebouças, T. F. Oliveira and F. R. Cunha

      Version of Record online: 16 NOV 2016 | DOI: 10.1002/fld.4346

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      A mesh relaxation method which completely removes the Lagrangian behavior of the Boundary Integral mesh was developed, allowing long-term simulations without significant mesh distortion, even for high viscosity ratio drops. The dependence of the mesh on the flowŠs history was monitored by computing the standard deviation of the elements areas along the simulations. An automatic time-step control method, based on the Drop Cauchy-Green tensor was created to accelerate time evolution and save computational time, without loss of accuracy.

    12. Finite element methods for a class of continuum models for immiscible flows with moving contact lines

      Arnold Reusken, Xianmin Xu and Liang Zhang

      Version of Record online: 15 NOV 2016 | DOI: 10.1002/fld.4349

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      We present a level-set based finite element method for two-phase incompressible flows with moving contact lines. We use a sharp interface model and consider a class of continuum models for describing the moving contact lines. A general variational formulation and a corresponding energy estimate are derived. The discontinuous pressure is accurately approximated by using a stabilized extended finite element space, and a Nitsche technique is applied to weakly impose the Navier boundary conditions.

  4. Research Paper Presented at MULTIMAT 2015

    1. Optimal control for reinitialization in finite element level set methods

      Christopher Basting, Dmitri Kuzmin and John N. Shadid

      Version of Record online: 14 NOV 2016 | DOI: 10.1002/fld.4348

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      A new reinitialization technique based on an optimal control approach is presented. The residual of the Eikonal equation is incorporated into the objective functional. The state equation is given by the level set transport equation but augmented by an additional source term. The method is evaluated numerically in three different examples and compared to other PDE-based reinitialization techniques.

  5. Research Articles

    1. An accurate pressure–velocity decoupling technique for semi-implicit rotational projection methods

      Ehsan Tavakoli

      Version of Record online: 10 NOV 2016 | DOI: 10.1002/fld.4347

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      Herein, we propose an accurate technique to decouple pressure from the momentum equation by incorporating the principle form of the pressure Poisson equation for semi-implicit projection methods. The velocity correction step is redefined, and boundary conditions are introduced accordingly. It is shown that the present method can preserve the order of accuracy for second-order and high-order finite difference simulations. A very good agreement is observed between the results of the present method and the benchmark simulations.

    2. Projection-based variational multiscale method for incompressible Navier–Stokes equations in time-dependent domains

      Birupaksha Pal and Sashikumaar Ganesan

      Version of Record online: 9 NOV 2016 | DOI: 10.1002/fld.4338

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      A projection-based variational multiscale method for computations of incompressible Navier–Stokes equations in time-dependent domains is presented. An arbitrary Lagrangian–Eulerian approach with an elastic mesh moving technique with mesh-dependent stiffness is tailored with the variational multiscale method to handle moving boundaries. Simulations of flow around a static beam attached to a square base, around an oscillating beam, and around a plunging aerofoil are presented.

  6. Research Paper Presented at MULTIMAT 2015

    1. An efficient high order direct ALE ADER finite volume scheme with a posteriori limiting for hydrodynamics and magnetohydrodynamics

      Walter Boscheri

      Version of Record online: 3 NOV 2016 | DOI: 10.1002/fld.4342

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      The arbitrary-Lagrangian-Eulerian ADER MOOD quadrature-free algorithm is a finite volume scheme that achieves high order of accuracy in space by limiting the reconstruction relying on the a posteriori MOOD strategy and reaches the same order of accuracy in time using the ADER approach. Efficiency is furthermore improved by a quadrature-free integration of the numerical fluxes. Hydrodynamics and magnetohydrodynamics equations are considered in multiple space dimensions on unstructured meshes in 2D and in 3D, and the speedup is monitored.

  7. Research Articles

    1. Acoustic simulation using a novel approach for reducing dispersion error

      G. Wang, X.Y. Cui and G.Y. Li

      Version of Record online: 20 OCT 2016 | DOI: 10.1002/fld.4339

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      A novel approach that combines Shepard interpolation and linear shape functions is proposed for reducing the dispersion error in acoustic analysis. For each independent element, the gradient field is formed based on the element itself and its adjacent elements sharing common edges (or faces). Theoretic analysis and numerical results illustrate that the present algorithm performs well in simulating high wavenumber problems.

    2. A robust low-dissipation AUSM-family scheme for numerical shock stability on unstructured grids

      Fan Zhang, Jun Liu, Biaosong Chen and Wanxie Zhong

      Version of Record online: 19 OCT 2016 | DOI: 10.1002/fld.4341

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      A hybrid upwind scheme is devised for improving the shock stability of SLAU scheme. The dissipation term of SLAU flux function is modified to give a new hybrid flux function. The hybrid flux function is used on the solution of momentum fluxes. In the test cases, the hybrid scheme is showing improvements on the numerical shock stability.

    3. Dissipation matrix and artificial heat conduction for Godunov-type schemes of compressible fluid flows

      Jiequan Li, Baolin Tian and Shuanghu Wang

      Version of Record online: 19 OCT 2016 | DOI: 10.1002/fld.4340

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      This paper aims to reassess the Riemann solver for compressible fluid flows in the Lagrangian frame from the viewpoint of modified equation approach and provides a theoretical insight into dissipation mechanism. It is observed that numerical dissipation vanishes uniformly for the Godunov-type schemes in the Lagrangian frame, which connects to some numerical defects such as the wall-heating phenomenon and start-up errors. To cure the defects, the artificial heat conduction, in addition to the traditional numerical viscosity, is introduced via a passage of the Lax–Friedrichs type discretization of internal energy.

    4. A robust flux splitting method with low dissipation for all-speed flows

      Di Sun, Chao Yan, Feng Qu and Ruofan Du

      Version of Record online: 12 OCT 2016 | DOI: 10.1002/fld.4337

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      We propose a robust flux splitting method with low dissipation for all speed flows. A low-dissipation modification is properly applied to the convection and the pressure parts of the inviscid terms of the Euler equation, respectively, which improves the accuracy obviously without enhancing the computational costs of the method. The results of this study prove that the new method can enhance the accuracy and robustness for solving all-speed flows.

    5. Investigation of the sensitivity of turbulent closures and coupling of hybrid RANS-LES models for predicting flow fields with separation and reattachment

      G. Kumar, S. K. Lakshmanan, H. Gopalan and A. De

      Version of Record online: 4 OCT 2016 | DOI: 10.1002/fld.4334

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      In this study, a generic non-linear blended modeling framework for performing hybrid RANS-LES simulations is proposed and flow over the periodic hills is used as the test case for model evaluation. Analysis of the simulations suggests that the non-linear closures are less sensitive to the RANS-LES coupling method and grid resolution. Also, good agreement has been found for flow statistics compared with the existing experimental data for simulations performed using NSST-Blended at higher Reynolds number.

    6. A mixed-interpolation finite element method for incompressible thermal flows of electrically conducting fluids

      Haruhiko Kohno

      Version of Record online: 4 OCT 2016 | DOI: 10.1002/fld.4292

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      A high-speed finite element scheme is proposed for simulation of incompressible MHD flows with convective heat transfer. In the proposed scheme, Q2-Q1 elements are used for the interpolations of the velocity, pressure, and temperature, while the electric field and magnetic flux density are interpolated using vector shape functions in the subdivided four-node elements. The robustness of the scheme is investigated using highly distorted meshes in well-known problems, and the results showing the improvement of calculation speed are also presented.

    7. Managing false diffusion during second-order upwind simulations of liquid micromixing

      Robert T. Bailey

      Version of Record online: 4 OCT 2016 | DOI: 10.1002/fld.4335

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      Numerical simulations were conducted to determine an ‘effective’ false diffusion coefficient (Dfalse) for the second-order upwind finite volume method. Expressions for estimating the spacing required to reduce Dfalse to some desired (low) level were incorporated into a procedure for managing false diffusion when simulating steady, liquid micromixing using structured and unstructured meshes.

  8. Research Paper Presented at MULTIMAT 2015

    1. A 3D finite volume scheme for solving the updated Lagrangian form of hyperelasticity

      G. Georges, J. Breil and P.-H. Maire

      Version of Record online: 29 SEP 2016 | DOI: 10.1002/fld.4336

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      This paper presents the 3D extension of the EUCCLHYD scheme (Explicit Unstructured Cell-Centered Lagrangian HYDrodynamics) [Maire SIAM 2007] for the numerical modeling of the hyperelasticity system at first order in space and time. The constitutive law is derived by means of a Coleman–Noll procedure in the case of isotropic neo-Hookean materials. The scheme is validated on three test cases and is proved to have an inherent 3D nature when shearing is present such as in the oscillating beam problem (refer to Figure 1).

  9. Research Articles

    1. A combined level set/ghost cell immersed boundary representation for floating body simulations

      H. Bihs and A. Kamath

      Version of Record online: 27 SEP 2016 | DOI: 10.1002/fld.4333

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      The paper discusses the implementation of a novel six degree of freedom (6DOF) algorithm in the open-source CFD code REEF3D. The new 6DOF algorithm makes re-meshing or overset grids unnecessary, resulting in a simpler, faster, and more stable algorithm. Several benchmark applications show that the new floating body algorithm can handle even impact scenarios in a weakly coupled manner while maintaining numerical stability and accuracy.

    2. Mono-block and non-matching multi-block structured mesh adaptation based on aerodynamic functional total derivatives for RANS flow

      A. Resmini, J. Peter and D. Lucor

      Version of Record online: 21 SEP 2016 | DOI: 10.1002/fld.4296

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      The paper presents an enhanced goal-oriented adjoint-based mesh adaptation method based on a scalar indicator for one mesh level only for RANS flows, where the linearization of the Spalart–Allmaras turbulence model is addressed. The adaptation procedure is assessed on standard monoblock and non-conforming multi-block-structured mesh with non-matching interfaces between blocks. The method is efficient for Euler and RANS flows, standard and non-conforming meshes, and transonic and detached subsonic operational flow conditions.

    3. Multi-scale time integration for transient conjugate heat transfer

      L. He and M. Fadl

      Version of Record online: 15 SEP 2016 | DOI: 10.1002/fld.4295

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      A new multi-scale framework in a triple-timing form is adopted to avoid the common quasi-steady flow assumption. Slow temporal variations corresponding to the solid time scales are included in the fluid domain as a source term, whilst short-scale fluid unsteadiness is captured by local time integration. The test case results indicate that a much enhanced applicability can be achieved by relatively small modifications of existing transient conjugate heat transfer methods.

    4. Stabilized mixed three-field formulation for a generalized incompressible Oldroyd-B model

      JaeHyuk Kwack, Arif Masud and K. R. Rajagopal

      Version of Record online: 15 SEP 2016 | DOI: 10.1002/fld.4287

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      A stabilized mixed formulation is developed for a generalized incompressible Oldroyd-B model that is based on a thermodynamically consistent framework for multiple natural configurations. The new method uniformly imposes the incompressibility condition on the elastic stretch tensor and shows optimal L2 convergence for the conformation tensor field on benchmark problems. This figure shows the magnitude of the elastic stretch tensor B and its rate of convergence for various element types.

    5. GPU-accelerated direct numerical simulations of decaying compressible turbulence employing a GKM-based solver

      Nishant Parashar, Balaji Srinivasan, Sawan Suman Sinha and Manish Agarwal

      Version of Record online: 8 SEP 2016 | DOI: 10.1002/fld.4291

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      Evaluation of the analytical gas kinetic method developed by Xuan and Xu (2013) is done in its performance to simulate decaying compressible turbulence on graphical processing unit (GPU)s. We find that analytical gas kinetic method results show excellent agreement with high-order accurate direct numerical simulation results. We perform GPU optimizations on NVIDIA K20 GPU, which boosts the speedup up-to 40x as compared with CPU computations.

    6. Turbulence modelling and role of compressibility on oil spilling from a damaged double hull tank

      Hao Yang, Shiqiang Yan, Qingwei Ma, Jinshu Lu and Yan Zhou

      Version of Record online: 7 SEP 2016 | DOI: 10.1002/fld.4294

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      The paper presents comparative studies on the turbulence modelling and the role of compressibility on oil spilling from DHTs. It suggests criterion to select the appropriate turbulence model in terms of computational robustness using the effective Reynolds number, considering both oil outflow and water inflow. It also concludes that the compressibility of the fluid may be considerable in a small temporal-spatial scale but plays insignificant role on macroscopic process of the oil spilling.

    7. A modified Galerkin/finite element method for the numerical solution of the Serre-Green-Naghdi system

      D. Mitsotakis, C. Synolakis and M. McGuinness

      Version of Record online: 6 SEP 2016 | DOI: 10.1002/fld.4293

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      A fully discrete numerical scheme for some fully-nonlinear shallow water equations with wall boundary conditions is developed. Shoaling and reflecting solitary waves are studied in detail. The accuracy and the efficiency of this numerical method is demonstrated while the match between numerical results, experimental data, and theoretical approximations is very satisfactory.

  10. Research Paper Presented at MULTIMAT 2015

    1. High-order discontinuous Galerkin nonlocal transport and energy equations scheme for radiation hydrodynamics

      M. Holec, J. Limpouch, R. Liska and S. Weber

      Version of Record online: 5 SEP 2016 | DOI: 10.1002/fld.4288

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      Nonlocal radiative transport in laser-heated plasmas of arbitrary Knudsen number is a challenging task. We directly solve the photon transport equation based on the Bhatnagar-Gross-Krook(BGK) collision operator, which gives an inherent coupling of radiation to the fluid plasma parameters. Our high-order discontinuous Galerkin scheme of the BGK transport equation and thefluid energy equation gives solutions obeying both limiting cases of transport, i.e. diffusion and free-streaming. As an application, we present simulation results of intense laser-target interaction.

    2. A fully discrete ALE method over untwisted time–space control volumes

      Jin Qi and Jiequan Li

      Version of Record online: 24 AUG 2016 | DOI: 10.1002/fld.4283

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      Our work is focused on two important technologies in ALE method:

      • The untwisted adaptively moving time–space control volume is generated only by the irrotational part of the flow velocity based on the Helmholtz theorem to avoid the mesh tangling.
      • The GRP solver with the whole wave configuration is employed for flux computation to ensure the high resolution.
    3. Divergence preserving reconstruction of the nodal components of a vector field from its normal components to edges

      Richard Liska and Mikhail Shashkov

      Version of Record online: 22 AUG 2016 | DOI: 10.1002/fld.4289

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      We have developed a new divergence preserving method for the reconstruction of the Cartesian components of a vector field from the orthogonal projection of a vector field to the normals to edges in 2D. The new global divergence preserving method is exact for linear vector fields.

    4. Study of a collocated Lagrange-remap scheme for multi-material flows adapted to HPC

      Jean-Philippe Braeunig and Bastien Chaudet

      Version of Record online: 17 AUG 2016 | DOI: 10.1002/fld.4286

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      In the context of a Eulerian Lagrange-remap scheme on planar geometry and for rectangular meshes, we propose and compare remapping schemes using a finite volume framework. We consider directional splitting or fully multi-dimensional remaps, and we focus on a definition of the so-called corner fluxes. We also address the issue of the internal energy behavior when using a conservative total energy remap.

  11. Research Articles

    1. A novel weighting switch function for uniformly high-order hybrid shock-capturing schemes

      Jun Peng and Yiqing Shen

      Version of Record online: 10 AUG 2016 | DOI: 10.1002/fld.4285

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      In this paper, a parameter-free weighting switch function is proposed for developing a family of high order hybrid schemes. As an example, a seventh-order hybrid compact-CRWENO scheme (HCCS) is constructed and analyzed with the proposed function. Numerical results show that the new scheme has very low dissipation and maintains the essentially non-oscillation property of the base-CRWENO scheme. As shown in this figure, HCCS is even more efficient than the seventh-order WENO scheme.

  12. Research Paper Presented at MULTIMAT 2015

    1. A 3D finite element ALE method using an approximate Riemann solution

      V. P. Chiravalle and N. R. Morgan

      Version of Record online: 9 AUG 2016 | DOI: 10.1002/fld.4284

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      A finite element arbitrary Lagrangian–Eulerian method that solves a multidirectional Riemann-like problem incorporating two limiting coefficients: the first is based on the minmod limiter and the second is a function of the discrete Mach number is presented. Our approach produces substantially less internal energy errors than the minmod limiter alone for a steel shell implosion as shown in Figure 1. For strong shock problems, the new limiter is more accurate and converges at a higher rate than the quadratic artificial viscosity.


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