Close Search Advanced
Journals
Resources
About Us
Open Access

A Novel Full-Euler Low Mach Number IMEX Splitting

A Novel Full-Euler Low Mach Number IMEX Splitting
Preview
Add to basket

Year:    2020

Author:    Jonas Zeifang, Jochen Schütz, Klaus Kaiser, Andrea Beck, Maria Lukáčová-Medvid'ová, Sebastian Noelle

Communications in Computational Physics, Vol. 27 (2020), Iss. 1 : pp. 292–320

Abstract

In this paper, we introduce an extension of a splitting method for singularly perturbed equations, the so-called RS-IMEX splitting [Kaiser et al., Journal of Scientific Computing, 70(3), 1390–1407], to deal with the fully compressible Euler equations. The straightforward application of the splitting yields sub-equations that are, due to the occurrence of complex eigenvalues, not hyperbolic. A modification, slightly changing the convective flux, is introduced that overcomes this issue. It is shown that the splitting gives rise to a discretization that respects the low-Mach number limit of the Euler equations; numerical results using finite volume and discontinuous Galerkin schemes show the potential of the discretization.

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.OA-2018-0270

Communications in Computational Physics, Vol. 27 (2020), Iss. 1 : pp. 292–320

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    29

Keywords:    Euler equations low-Mach IMEX Runge-Kutta RS-IMEX.

Author Details

Jonas Zeifang

Jochen Schütz

Klaus Kaiser

Andrea Beck

Maria Lukáčová-Medvid'ová

Sebastian Noelle

  1. An all Mach number scheme for visco-resistive magnetically-dominated MHD flows

    Dematté, Riccardo | Farmakalides, Alexander A. | Millmore, Stephen | Nikiforakis, Nikos

    Journal of Computational Physics, Vol. 514 (2024), Iss. P.113229

    https://doi.org/10.1016/j.jcp.2024.113229 [Citations: 0]

  2. High Order Semi-implicit WENO Schemes for All-Mach Full Euler System of Gas Dynamics

    Boscarino, Sebastiano | Qiu, Jingmei | Russo, Giovanni | Xiong, Tao

    SIAM Journal on Scientific Computing, Vol. 44 (2022), Iss. 2 P.B368

    https://doi.org/10.1137/21M1424433 [Citations: 17]

  3. TVD-MOOD schemes based on implicit-explicit time integration

    Michel-Dansac, Victor | Thomann, Andrea

    Applied Mathematics and Computation, Vol. 433 (2022), Iss. P.127397

    https://doi.org/10.1016/j.amc.2022.127397 [Citations: 2]

  4. Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations

    Kučera, Václav | Lukáčová-Medvid’ová, Mária | Noelle, Sebastian | Schütz, Jochen

    Numerische Mathematik, Vol. 150 (2022), Iss. 1 P.79

    https://doi.org/10.1007/s00211-021-01240-5 [Citations: 3]

  5. A novel approach to the characteristic splitting scheme for mildly compressible flows based on the weighted averaged flux method

    Fiolitakis, A. | Pries, M.

    Journal of Computational Physics, Vol. 513 (2024), Iss. P.113197

    https://doi.org/10.1016/j.jcp.2024.113197 [Citations: 0]

  6. A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method

    Zeifang, Jonas | Beck, Andrea

    Communications on Applied Mathematics and Computation, Vol. 5 (2023), Iss. 2 P.722

    https://doi.org/10.1007/s42967-021-00137-2 [Citations: 1]

  7. Implicit finite volume method with a posteriori limiting for transport networks

    Eimer, Matthias | Borsche, Raul | Siedow, Norbert

    Advances in Computational Mathematics, Vol. 48 (2022), Iss. 3

    https://doi.org/10.1007/s10444-022-09939-1 [Citations: 2]

  8. A Well-Balanced Asymptotic Preserving Scheme for the Two-Dimensional Rotating Shallow Water Equations with Nonflat Bottom Topography

    Kurganov, Alexander | Liu, Yongle | Lukáčová-Medviďová, Mária

    SIAM Journal on Scientific Computing, Vol. 44 (2022), Iss. 3 P.A1655

    https://doi.org/10.1137/21M141573X [Citations: 4]

  9. An all Mach number finite volume method for isentropic two-phase flow

    Lukáčová-Medvid’ová, Mária | Puppo, Gabriella | Thomann, Andrea

    Journal of Numerical Mathematics, Vol. 31 (2023), Iss. 3 P.175

    https://doi.org/10.1515/jnma-2022-0015 [Citations: 12]

  10. Implicit Relaxed All Mach Number Schemes for Gases and Compressible Materials

    Thomann, Andrea | Iollo, Angelo | Puppo, Gabriella

    SIAM Journal on Scientific Computing, Vol. 45 (2023), Iss. 5 P.A2632

    https://doi.org/10.1137/21M146819X [Citations: 1]

  11. An efficient IMEX-DG solver for the compressible Navier-Stokes equations for non-ideal gases

    Orlando, Giuseppe | Barbante, Paolo Francesco | Bonaventura, Luca

    Journal of Computational Physics, Vol. 471 (2022), Iss. P.111653

    https://doi.org/10.1016/j.jcp.2022.111653 [Citations: 11]

  12. High order well-balanced asymptotic preserving IMEX RKDG schemes for the two-dimensional nonlinear shallow water equations

    Xie, Xian | Dong, Haiyun | Li, Maojun

    Journal of Computational Physics, Vol. 510 (2024), Iss. P.113092

    https://doi.org/10.1016/j.jcp.2024.113092 [Citations: 0]

  13. Parallel-in-Time High-Order Multiderivative IMEX Solvers

    Schütz, Jochen | Seal, David C. | Zeifang, Jonas

    Journal of Scientific Computing, Vol. 90 (2022), Iss. 1

    https://doi.org/10.1007/s10915-021-01733-3 [Citations: 5]

  14. Compressible Navier–Stokes Equations with Potential Temperature Transport: Stability of the Strong Solution and Numerical Error Estimates

    Lukáčová-Medvid’ová, Mária | Schömer, Andreas

    Journal of Mathematical Fluid Mechanics, Vol. 25 (2023), Iss. 1

    https://doi.org/10.1007/s00021-022-00733-z [Citations: 3]
  15. Recent Advances in Numerical Methods for Hyperbolic PDE Systems

    Recent Advances and Complex Applications of the Compressible Ghost-Fluid Method

    Jöns, Steven | Müller, Christoph | Zeifang, Jonas | Munz, Claus-Dieter

    2021

    https://doi.org/10.1007/978-3-030-72850-2_7 [Citations: 5]

  16. An efficient second order all Mach finite volume solver for the compressible Navier–Stokes equations

    Boscheri, Walter | Dimarco, Giacomo | Tavelli, Maurizio

    Computer Methods in Applied Mechanics and Engineering, Vol. 374 (2021), Iss. P.113602

    https://doi.org/10.1016/j.cma.2020.113602 [Citations: 27]

  17. An implicit-explicit solver for a two-fluid single-temperature model

    Lukáčová-Medvid'ová, Mária | Peshkov, Ilya | Thomann, Andrea

    Journal of Computational Physics, Vol. 498 (2024), Iss. P.112696

    https://doi.org/10.1016/j.jcp.2023.112696 [Citations: 2]

  18. An asymptotic preserving semi-implicit multiderivative solver

    Schütz, Jochen | Seal, David C.

    Applied Numerical Mathematics, Vol. 160 (2021), Iss. P.84

    https://doi.org/10.1016/j.apnum.2020.09.004 [Citations: 10]

  19. High order well-balanced asymptotic preserving finite difference WENO schemes for the shallow water equations in all Froude numbers

    Huang, Guanlan | Xing, Yulong | Xiong, Tao

    Journal of Computational Physics, Vol. 463 (2022), Iss. P.111255

    https://doi.org/10.1016/j.jcp.2022.111255 [Citations: 13]

  20. Time parallelism and Newton-adaptivity of the two-derivative deferred correction discontinuous Galerkin method

    Zeifang, Jonas | Thenery Manikantan, Arjun | Schütz, Jochen

    Applied Mathematics and Computation, Vol. 457 (2023), Iss. P.128198

    https://doi.org/10.1016/j.amc.2023.128198 [Citations: 3]

  21. Schur complement IMplicit-EXplicit formulations for discontinuous Galerkin non-hydrostatic atmospheric models

    Reddy, Sohail | Waruszewski, Maciej | de Braganca Alves, Felipe A.V. | Giraldo, Francis X.

    Journal of Computational Physics, Vol. 491 (2023), Iss. P.112361

    https://doi.org/10.1016/j.jcp.2023.112361 [Citations: 3]

  22. Recasting an operator splitting solver into a standard finite volume flux-based algorithm. The case of a Lagrange-projection-type method for gas dynamics

    Bourgeois, Rémi | Tremblin, Pascal | Kokh, Samuel | Padioleau, Thomas

    Journal of Computational Physics, Vol. 496 (2024), Iss. P.112594

    https://doi.org/10.1016/j.jcp.2023.112594 [Citations: 2]

  23. High resolution compact implicit numerical scheme for conservation laws

    Frolkovič, Peter | Žeravý, Michal

    Applied Mathematics and Computation, Vol. 442 (2023), Iss. P.127720

    https://doi.org/10.1016/j.amc.2022.127720 [Citations: 3]

  24. Implicit two-derivative deferred correction time discretization for the discontinuous Galerkin method

    Zeifang, Jonas | Schütz, Jochen

    Journal of Computational Physics, Vol. 464 (2022), Iss. P.111353

    https://doi.org/10.1016/j.jcp.2022.111353 [Citations: 9]

  25. A second order all Mach number IMEX finite volume solver for the three dimensional Euler equations

    Boscheri, Walter | Dimarco, Giacomo | Loubère, Raphaël | Tavelli, Maurizio | Vignal, Marie-Hélène

    Journal of Computational Physics, Vol. 415 (2020), Iss. P.109486

    https://doi.org/10.1016/j.jcp.2020.109486 [Citations: 34]