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.
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
-
An all Mach number scheme for visco-resistive magnetically-dominated MHD flows
Dematté, Riccardo | Farmakalides, Alexander A. | Millmore, Stephen | Nikiforakis, NikosJournal of Computational Physics, Vol. 514 (2024), Iss. P.113229
https://doi.org/10.1016/j.jcp.2024.113229 [Citations: 0] -
High Order Semi-implicit WENO Schemes for All-Mach Full Euler System of Gas Dynamics
Boscarino, Sebastiano | Qiu, Jingmei | Russo, Giovanni | Xiong, TaoSIAM Journal on Scientific Computing, Vol. 44 (2022), Iss. 2 P.B368
https://doi.org/10.1137/21M1424433 [Citations: 17] -
TVD-MOOD schemes based on implicit-explicit time integration
Michel-Dansac, Victor | Thomann, AndreaApplied Mathematics and Computation, Vol. 433 (2022), Iss. P.127397
https://doi.org/10.1016/j.amc.2022.127397 [Citations: 2] -
Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations
Kučera, Václav | Lukáčová-Medvid’ová, Mária | Noelle, Sebastian | Schütz, JochenNumerische Mathematik, Vol. 150 (2022), Iss. 1 P.79
https://doi.org/10.1007/s00211-021-01240-5 [Citations: 4] -
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] -
A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method
Zeifang, Jonas | Beck, AndreaCommunications on Applied Mathematics and Computation, Vol. 5 (2023), Iss. 2 P.722
https://doi.org/10.1007/s42967-021-00137-2 [Citations: 1] -
Implicit finite volume method with a posteriori limiting for transport networks
Eimer, Matthias | Borsche, Raul | Siedow, NorbertAdvances in Computational Mathematics, Vol. 48 (2022), Iss. 3
https://doi.org/10.1007/s10444-022-09939-1 [Citations: 2] -
A Well-Balanced Asymptotic Preserving Scheme for the Two-Dimensional Rotating Shallow Water Equations with Nonflat Bottom Topography
Kurganov, Alexander | Liu, Yongle | Lukáčová-Medviďová, MáriaSIAM Journal on Scientific Computing, Vol. 44 (2022), Iss. 3 P.A1655
https://doi.org/10.1137/21M141573X [Citations: 4] -
An all Mach number finite volume method for isentropic two-phase flow
Lukáčová-Medvid’ová, Mária | Puppo, Gabriella | Thomann, AndreaJournal of Numerical Mathematics, Vol. 31 (2023), Iss. 3 P.175
https://doi.org/10.1515/jnma-2022-0015 [Citations: 12] -
Implicit Relaxed All Mach Number Schemes for Gases and Compressible Materials
Thomann, Andrea | Iollo, Angelo | Puppo, GabriellaSIAM Journal on Scientific Computing, Vol. 45 (2023), Iss. 5 P.A2632
https://doi.org/10.1137/21M146819X [Citations: 1] -
An efficient IMEX-DG solver for the compressible Navier-Stokes equations for non-ideal gases
Orlando, Giuseppe | Barbante, Paolo Francesco | Bonaventura, LucaJournal of Computational Physics, Vol. 471 (2022), Iss. P.111653
https://doi.org/10.1016/j.jcp.2022.111653 [Citations: 13] -
High order well-balanced asymptotic preserving IMEX RKDG schemes for the two-dimensional nonlinear shallow water equations
Xie, Xian | Dong, Haiyun | Li, MaojunJournal of Computational Physics, Vol. 510 (2024), Iss. P.113092
https://doi.org/10.1016/j.jcp.2024.113092 [Citations: 0] -
Parallel-in-Time High-Order Multiderivative IMEX Solvers
Schütz, Jochen | Seal, David C. | Zeifang, JonasJournal of Scientific Computing, Vol. 90 (2022), Iss. 1
https://doi.org/10.1007/s10915-021-01733-3 [Citations: 5] -
Compressible Navier–Stokes Equations with Potential Temperature Transport: Stability of the Strong Solution and Numerical Error Estimates
Lukáčová-Medvid’ová, Mária | Schömer, AndreasJournal of Mathematical Fluid Mechanics, Vol. 25 (2023), Iss. 1
https://doi.org/10.1007/s00021-022-00733-z [Citations: 3] -
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-Dieter2021
https://doi.org/10.1007/978-3-030-72850-2_7 [Citations: 5] -
An efficient second order all Mach finite volume solver for the compressible Navier–Stokes equations
Boscheri, Walter | Dimarco, Giacomo | Tavelli, MaurizioComputer Methods in Applied Mechanics and Engineering, Vol. 374 (2021), Iss. P.113602
https://doi.org/10.1016/j.cma.2020.113602 [Citations: 27] -
An implicit-explicit solver for a two-fluid single-temperature model
Lukáčová-Medvid'ová, Mária | Peshkov, Ilya | Thomann, AndreaJournal of Computational Physics, Vol. 498 (2024), Iss. P.112696
https://doi.org/10.1016/j.jcp.2023.112696 [Citations: 3] -
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] -
High order well-balanced asymptotic preserving finite difference WENO schemes for the shallow water equations in all Froude numbers
Huang, Guanlan | Xing, Yulong | Xiong, TaoJournal of Computational Physics, Vol. 463 (2022), Iss. P.111255
https://doi.org/10.1016/j.jcp.2022.111255 [Citations: 13] -
Time parallelism and Newton-adaptivity of the two-derivative deferred correction discontinuous Galerkin method
Zeifang, Jonas | Thenery Manikantan, Arjun | Schütz, JochenApplied Mathematics and Computation, Vol. 457 (2023), Iss. P.128198
https://doi.org/10.1016/j.amc.2023.128198 [Citations: 3] -
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] -
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, ThomasJournal of Computational Physics, Vol. 496 (2024), Iss. P.112594
https://doi.org/10.1016/j.jcp.2023.112594 [Citations: 2] -
High resolution compact implicit numerical scheme for conservation laws
Frolkovič, Peter | Žeravý, MichalApplied Mathematics and Computation, Vol. 442 (2023), Iss. P.127720
https://doi.org/10.1016/j.amc.2022.127720 [Citations: 3] -
Implicit two-derivative deferred correction time discretization for the discontinuous Galerkin method
Zeifang, Jonas | Schütz, JochenJournal of Computational Physics, Vol. 464 (2022), Iss. P.111353
https://doi.org/10.1016/j.jcp.2022.111353 [Citations: 9] -
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-HélèneJournal of Computational Physics, Vol. 415 (2020), Iss. P.109486
https://doi.org/10.1016/j.jcp.2020.109486 [Citations: 34]