research-article

Mass Flux Schemes and Connection to Shock Instability

Author:

Meng-Sing LiouAuthors Info & Claims

Journal of Computational Physics, Volume 160, Issue 2

Pages 623 - 648

https://doi.org/10.1006/jcph.2000.6478

Published: 20 May 2000 Publication History

Abstract

We analyze numerical mass fluxes with an emphasis on their capability for accurately capturing shock and contact discontinuities. The study of mass flux is useful because it is the term common to all conservation equations and the numerical diffusivity introduced in it bears a direct consequence to the prediction of contact (stationary and moving) discontinuities, which are considered to be the limiting case of the boundary layer. We examine several prominent numerical flux schemes and analyze the structure of numerical diffusivity. This leads to a detailed investigation into the cause of certain catastrophic breakdowns by some numerical flux schemes. In particular, we identify the dissipative terms that are responsible for shock instabilities, such as the odd even decoupling and the so-called “carbuncle phenomenon”. As a result, we propose a conjecture stating the connection of the pressure difference term to these multidimensional shock instabilities and hence a cure to those difficulties. The validity of this conjecture has been confirmed by examining a wide class of upwind schemes. The conjecture is useful to the flux function development, for it indicates whether the flux scheme under consideration will be afflicted with these kinds of failings. Thus, a class of shock-stable schemes can be identified. Interestingly, a shock-stable scheme's self-correcting capability is demonstrated with respect to carbuncle-contaminated profiles for flows at both low supersonic and high Mach numbers.

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Cited By

Gogoi AMandal JSaraf A(2025)Stability evaluation of approximate Riemann solvers using the direct Lyapunov methodJournal of Computational Physics10.1016/j.jcp.2024.113599522:COnline publication date: 1-Feb-2025
https://dl.acm.org/doi/10.1016/j.jcp.2024.113599
Hu LTan SLi LYuan H(2023)An accurate, robust and efficient convection-pressure flux splitting scheme for compressible Euler flowsJournal of Computational Physics10.1016/j.jcp.2023.112505493:COnline publication date: 15-Nov-2023
https://dl.acm.org/doi/10.1016/j.jcp.2023.112505
Chen SLi JYuan WGao Z(2023)Nonlinear entropy stable Riemann solver with heuristic logarithmic pressure augmentation for supersonic and hypersonic flowsComputers & Mathematics with Applications10.1016/j.camwa.2023.03.024141:C(33-41)Online publication date: 1-Jul-2023
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Index Terms

Mass Flux Schemes and Connection to Shock Instability
1. Applied computing
  1. Physical sciences and engineering
    1. Physics
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis

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Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 160, Issue 2

May 2000

381 pages

ISSN:0021-9991

Editor:
J. U. Brackbill
Los Alamos National Lab., Los Alamos, NM

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Publisher

Academic Press Professional, Inc.

United States

Publication History

Published: 20 May 2000

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Cited By

Gogoi AMandal JSaraf A(2025)Stability evaluation of approximate Riemann solvers using the direct Lyapunov methodJournal of Computational Physics10.1016/j.jcp.2024.113599522:COnline publication date: 1-Feb-2025
https://dl.acm.org/doi/10.1016/j.jcp.2024.113599
Hu LTan SLi LYuan H(2023)An accurate, robust and efficient convection-pressure flux splitting scheme for compressible Euler flowsJournal of Computational Physics10.1016/j.jcp.2023.112505493:COnline publication date: 15-Nov-2023
https://dl.acm.org/doi/10.1016/j.jcp.2023.112505
Chen SLi JYuan WGao Z(2023)Nonlinear entropy stable Riemann solver with heuristic logarithmic pressure augmentation for supersonic and hypersonic flowsComputers & Mathematics with Applications10.1016/j.camwa.2023.03.024141:C(33-41)Online publication date: 1-Jul-2023
https://dl.acm.org/doi/10.1016/j.camwa.2023.03.024
Chernykh IMisilov VAkimova EKulikov I(2023)The Effect of Data Structuring on the Parallel Efficiency of the HydroBox3D Relativistic CodeSupercomputing10.1007/978-3-031-49432-1_21(271-284)Online publication date: 25-Sep-2023
https://dl.acm.org/doi/10.1007/978-3-031-49432-1_21
Minoshima TMiyoshi T(2021)A low-dissipation HLLD approximate Riemann solver for a very wide range of Mach numbersJournal of Computational Physics10.1016/j.jcp.2021.110639446:COnline publication date: 1-Dec-2021
https://dl.acm.org/doi/10.1016/j.jcp.2021.110639
Chen SYan CLin BLiu LYu J(2018)Affordable shock-stable item for Godunov-type schemes against carbuncle phenomenonJournal of Computational Physics10.1016/j.jcp.2018.07.022373:C(662-672)Online publication date: 15-Nov-2018
https://dl.acm.org/doi/10.1016/j.jcp.2018.07.022
Chen SYan CLin BLi Y(2018)A New Robust Carbuncle-Free Roe Scheme for Strong ShockJournal of Scientific Computing10.1007/s10915-018-0747-177:2(1250-1277)Online publication date: 1-Nov-2018
https://dl.acm.org/doi/10.1007/s10915-018-0747-1
Xie WLi WLi HTian ZPan S(2017)On numerical instabilities of Godunov-type schemes for strong shocksJournal of Computational Physics10.1016/j.jcp.2017.08.063350:C(607-637)Online publication date: 1-Dec-2017
https://dl.acm.org/doi/10.1016/j.jcp.2017.08.063
Rodionov A(2017)Artificial viscosity in Godunov-type schemes to cure the carbuncle phenomenonJournal of Computational Physics10.1016/j.jcp.2017.05.024345:C(308-329)Online publication date: 15-Sep-2017
https://dl.acm.org/doi/10.1016/j.jcp.2017.05.024
Shen ZYan WYuan G(2016)A robust HLLC-type Riemann solver for strong shockJournal of Computational Physics10.1016/j.jcp.2016.01.001309:C(185-206)Online publication date: 15-Mar-2016
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