Close Search Advanced
Journals
Resources
About Us
Open Access

Entropy Stable Scheme on Two-Dimensional Unstructured Grids for Euler Equations

Entropy Stable Scheme on Two-Dimensional Unstructured Grids for Euler Equations
Preview
Add to basket

Year:    2016

Communications in Computational Physics, Vol. 19 (2016), Iss. 5 : pp. 1111–1140

Abstract

We propose an entropy stable high-resolution finite volume scheme to approximate systems of two-dimensional symmetrizable conservation laws on unstructured grids. In particular we consider Euler equations governing compressible flows. The scheme is constructed using a combination of entropy conservative fluxes and entropy-stable numerical dissipation operators. High resolution is achieved based on a linear reconstruction procedure satisfying a suitable sign property that helps to maintain entropy stability. The proposed scheme is demonstrated to robustly approximate complex flow features by a series of benchmark numerical experiments.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.scpde14.43s

Communications in Computational Physics, Vol. 19 (2016), Iss. 5 : pp. 1111–1140

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    30

Keywords:   

  1. A New Thermodynamically Compatible Finite Volume Scheme for Lagrangian Gas Dynamics

    Boscheri, Walter | Dumbser, Michael | Maire, Pierre-Henri

    SIAM Journal on Scientific Computing, Vol. 46 (2024), Iss. 4 P.A2224

    https://doi.org/10.1137/23M1580863 [Citations: 0]

  2. Skew-Symmetric Entropy Stable Modal Discontinuous Galerkin Formulations

    Chan, Jesse

    Journal of Scientific Computing, Vol. 81 (2019), Iss. 1 P.459

    https://doi.org/10.1007/s10915-019-01026-w [Citations: 23]

  3. Entropy stabilization and property-preserving limiters for ℙ1 discontinuous Galerkin discretizations of scalar hyperbolic problems

    Kuzmin, Dmitri

    Journal of Numerical Mathematics, Vol. 29 (2021), Iss. 4 P.307

    https://doi.org/10.1515/jnma-2020-0056 [Citations: 12]
  4. Numerical Simulation in Physics and Engineering: Trends and Applications

    Consistent Internal Energy Based Schemes for the Compressible Euler Equations

    Gallouët, T. | Herbin, R. | Latché, J. -C. | Therme, N.

    2021

    https://doi.org/10.1007/978-3-030-62543-6_3 [Citations: 1]

  5. Algebraic entropy fixes and convex limiting for continuous finite element discretizations of scalar hyperbolic conservation laws

    Kuzmin, Dmitri | Quezada de Luna, Manuel

    Computer Methods in Applied Mechanics and Engineering, Vol. 372 (2020), Iss. P.113370

    https://doi.org/10.1016/j.cma.2020.113370 [Citations: 11]

  6. A New Family of Thermodynamically Compatible Discontinuous Galerkin Methods for Continuum Mechanics and Turbulent Shallow Water Flows

    Busto, Saray | Dumbser, Michael

    Journal of Scientific Computing, Vol. 93 (2022), Iss. 2

    https://doi.org/10.1007/s10915-022-02017-0 [Citations: 2]

  7. A simple and general framework for the construction of thermodynamically compatible schemes for computational fluid and solid mechanics

    Abgrall, Rémi | Busto, Saray | Dumbser, Michael

    Applied Mathematics and Computation, Vol. 440 (2023), Iss. P.127629

    https://doi.org/10.1016/j.amc.2022.127629 [Citations: 8]
  8. Numerical Approximation of Hyperbolic Systems of Conservation Laws

    The Case of Multidimensional Systems

    Godlewski, Edwige | Raviart, Pierre-Arnaud

    2021

    https://doi.org/10.1007/978-1-0716-1344-3_5 [Citations: 0]

  9. Entropy stable numerical approximations for the isothermal and polytropic Euler equations

    Winters, Andrew R. | Czernik, Christof | Schily, Moritz B. | Gassner, Gregor J.

    BIT Numerical Mathematics, Vol. 60 (2020), Iss. 3 P.791

    https://doi.org/10.1007/s10543-019-00789-w [Citations: 9]

  10. Deep learning observables in computational fluid dynamics

    Lye, Kjetil O. | Mishra, Siddhartha | Ray, Deep

    Journal of Computational Physics, Vol. 410 (2020), Iss. P.109339

    https://doi.org/10.1016/j.jcp.2020.109339 [Citations: 92]

  11. Entropy stable essentially nonoscillatory methods based on RBF reconstruction

    Hesthaven, Jan S. | Mönkeberg, Fabian

    ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 53 (2019), Iss. 3 P.925

    https://doi.org/10.1051/m2an/2019011 [Citations: 18]

  12. On the robustness and performance of entropy stable collocated discontinuous Galerkin methods

    Rojas, Diego | Boukharfane, Radouan | Dalcin, Lisandro | Del Rey Fernández, David C. | Ranocha, Hendrik | Keyes, David E. | Parsani, Matteo

    Journal of Computational Physics, Vol. 426 (2021), Iss. P.109891

    https://doi.org/10.1016/j.jcp.2020.109891 [Citations: 21]

  13. On discretely entropy conservative and entropy stable discontinuous Galerkin methods

    Chan, Jesse

    Journal of Computational Physics, Vol. 362 (2018), Iss. P.346

    https://doi.org/10.1016/j.jcp.2018.02.033 [Citations: 101]

  14. A multi-level procedure for enhancing accuracy of machine learning algorithms

    LYE, KJETIL O. | MISHRA, SIDDHARTHA | MOLINARO, ROBERTO

    European Journal of Applied Mathematics, Vol. 32 (2021), Iss. 3 P.436

    https://doi.org/10.1017/S0956792520000224 [Citations: 18]
  15. Recent Advances in Numerical Methods for Hyperbolic PDE Systems

    Entropy Stable Numerical Fluxes for Compressible Euler Equations Which Are Suitable for All Mach Numbers

    Berberich, Jonas P. | Klingenberg, Christian

    2021

    https://doi.org/10.1007/978-3-030-72850-2_8 [Citations: 0]

  16. Entropy stable scheme for ideal MHD equations on adaptive unstructured meshes

    Zhang, Chengzhi | Zheng, Supei | Feng, Jianhu | Liu, Shasha

    Computers & Fluids, Vol. 285 (2024), Iss. P.106445

    https://doi.org/10.1016/j.compfluid.2024.106445 [Citations: 0]
  18. Handbook of Numerical Methods for Hyperbolic Problems - Basic and Fundamental Issues

    Entropy Stable Schemes

    Tadmor, E.

    2016

    https://doi.org/10.1016/bs.hna.2016.09.006 [Citations: 20]

  19. Entropy conserving/stable schemes for a vector-kinetic model of hyperbolic systems

    Anandan, Megala | Raghurama Rao, S.V.

    Applied Mathematics and Computation, Vol. 465 (2024), Iss. P.128410

    https://doi.org/10.1016/j.amc.2023.128410 [Citations: 1]

  20. A New Thermodynamically Compatible Finite Volume Scheme for Magnetohydrodynamics

    Busto, Saray | Dumbser, Michael

    SIAM Journal on Numerical Analysis, Vol. 61 (2023), Iss. 1 P.343

    https://doi.org/10.1137/22M147815X [Citations: 12]

  21. An Entropy Stable Scheme for Shallow Water Equations Based on Entropy Conservative Scheme

    张, 志壮

    Advances in Applied Mathematics, Vol. 11 (2022), Iss. 08 P.5648

    https://doi.org/10.12677/AAM.2022.118596 [Citations: 0]

  22. The scaled entropy variables reconstruction for entropy stable schemes with application to shallow water equations

    Liu, Qingsheng | Liu, Youqiong | Feng, Jianhu

    Computers & Fluids, Vol. 192 (2019), Iss. P.104266

    https://doi.org/10.1016/j.compfluid.2019.104266 [Citations: 4]

  23. Staggered-grid entropy-stable multidimensional summation-by-parts discretizations on curvilinear coordinates

    Del Rey Fernández, David C. | Crean, Jared | Carpenter, Mark H. | Hicken, Jason E.

    Journal of Computational Physics, Vol. 392 (2019), Iss. P.161

    https://doi.org/10.1016/j.jcp.2019.04.029 [Citations: 23]

  24. An Entropy-stable Ideal EC-GLM-MHD Model for the Simulation of the Three-dimensional Ambient Solar Wind

    Li, Caixia | Feng, Xueshang | Wei, Fengsi

    The Astrophysical Journal Supplement Series, Vol. 257 (2021), Iss. 2 P.24

    https://doi.org/10.3847/1538-4365/ac16d5 [Citations: 3]

  25. Entropy Stable Finite Difference Schemes for Compressible Euler Equations

    周, 翔宇

    Advances in Applied Mathematics, Vol. 11 (2022), Iss. 09 P.6331

    https://doi.org/10.12677/AAM.2022.119669 [Citations: 0]

  26. High-order accurate entropy stable adaptive moving mesh finite difference schemes for special relativistic (magneto)hydrodynamics

    Duan, Junming | Tang, Huazhong

    Journal of Computational Physics, Vol. 456 (2022), Iss. P.111038

    https://doi.org/10.1016/j.jcp.2022.111038 [Citations: 11]

  27. Limiter-based entropy stabilization of semi-discrete and fully discrete schemes for nonlinear hyperbolic problems

    Kuzmin, Dmitri | Hajduk, Hennes | Rupp, Andreas

    Computer Methods in Applied Mechanics and Engineering, Vol. 389 (2022), Iss. P.114428

    https://doi.org/10.1016/j.cma.2021.114428 [Citations: 18]

  28. High order entropy preserving ADER-DG schemes

    Gaburro, Elena | Öffner, Philipp | Ricchiuto, Mario | Torlo, Davide

    Applied Mathematics and Computation, Vol. 440 (2023), Iss. P.127644

    https://doi.org/10.1016/j.amc.2022.127644 [Citations: 12]

  29. Entropy-stable p-nonconforming discretizations with the summation-by-parts property for the compressible Navier–Stokes equations

    Fernández, David C. Del Rey | Carpenter, Mark H. | Dalcin, Lisandro | Fredrich, Lucas | Winters, Andrew R. | Gassner, Gregor J. | Parsani, Matteo

    Computers & Fluids, Vol. 210 (2020), Iss. P.104631

    https://doi.org/10.1016/j.compfluid.2020.104631 [Citations: 8]

  30. Global entropy stability for a class of unlimited second-order schemes for 2D hyperbolic systems of conservation laws on unstructured meshes

    Martaud, Ludovic

    Journal of Computational Physics, Vol. 487 (2023), Iss. P.112176

    https://doi.org/10.1016/j.jcp.2023.112176 [Citations: 0]

  31. Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws

    Chen, Tianheng | Shu, Chi-Wang

    Journal of Computational Physics, Vol. 345 (2017), Iss. P.427

    https://doi.org/10.1016/j.jcp.2017.05.025 [Citations: 164]

  32. Entropy Stable Schemes For Ten-Moment Gaussian Closure Equations

    Sen, Chhanda | Kumar, Harish

    Journal of Scientific Computing, Vol. 75 (2018), Iss. 2 P.1128

    https://doi.org/10.1007/s10915-017-0579-4 [Citations: 11]

  33. Entropy stable reduced order modeling of nonlinear conservation laws

    Chan, Jesse

    Journal of Computational Physics, Vol. 423 (2020), Iss. P.109789

    https://doi.org/10.1016/j.jcp.2020.109789 [Citations: 26]

  34. A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes

    Abgrall, R.

    Journal of Computational Physics, Vol. 372 (2018), Iss. P.640

    https://doi.org/10.1016/j.jcp.2018.06.031 [Citations: 57]

  35. An entropy stable finite volume scheme for the two dimensional Navier–Stokes equations on triangular grids

    Ray, Deep | Chandrashekar, Praveen

    Applied Mathematics and Computation, Vol. 314 (2017), Iss. P.257

    https://doi.org/10.1016/j.amc.2017.07.020 [Citations: 3]

  36. A New Class of Simple, General and Efficient Finite Volume Schemes for Overdetermined Thermodynamically Compatible Hyperbolic Systems

    Busto, Saray | Dumbser, Michael

    Communications on Applied Mathematics and Computation, Vol. 6 (2024), Iss. 3 P.1742

    https://doi.org/10.1007/s42967-023-00307-4 [Citations: 3]

  37. Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics

    Derigs, Dominik | Gassner, Gregor J. | Walch, Stefanie | Winters, Andrew R.

    Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 120 (2018), Iss. 3 P.153

    https://doi.org/10.1365/s13291-018-0178-9 [Citations: 6]