research-article

Effective low-Mach number improvement for upwind schemes

Authors:

Shu-sheng Chen,

Xing-hao XiangAuthors Info & Claims

Volume 75, Issue 10

Pages 3737 - 3755

https://doi.org/10.1016/j.camwa.2018.02.028

Published: 15 May 2018 Publication History

Abstract

In this paper, we present an effective low-Mach number improvement for upwind schemes. The artificial viscosity of upwind schemes scales with 1 ∕ M a incurring a loss of accuracy for the Mach number approaching zero. The remedy is based on three steps: (i) the jump of the left and right states is split into the density diffusion part and velocity diffusion part; (ii) the velocity diffusion part is rescaled by multiplying a scaling function; (iii) the scaling function is only related to the local Mach number without the cut-off reference Mach number and meantime restricted by a shock senor. The resulting modification is very easily implemented and applied within Roe, HLL and Rusanov, etc. Then, asymptotic analysis and numerical experiments for a wide Mach number demonstrate that this novel approach is equipped with these attractive properties: (1) free from the cut-off global problem and damping checkerboard modes; (2) satisfying the correct M a 2 scaling of pressure fluctuations, the divergence constraint and a Poisson equation; (3) independent of Mach number in terms of accuracy; (4) better accurate and higher resolution in low Mach number regimes when compared with existing upwind schemes, and applicable for moderate or high Mach numbers. Thus, the proposed modification is expected to provide as an excellent and reliable candidate to simulate turbulent flows at all Mach numbers.

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Published In

cover image Computers & Mathematics with Applications

Computers & Mathematics with Applications Volume 75, Issue 10

May 2018

374 pages

ISSN:0898-1221

Issue’s Table of Contents

Elsevier Ltd.

Publisher

Pergamon Press, Inc.

United States

Publication History

Published: 15 May 2018

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https://dl.acm.org/doi/10.1016/j.jcp.2024.112764
Lukáčová-Medvid'ová MPeshkov IThomann A(2024)An implicit-explicit solver for a two-fluid single-temperature modelJournal of Computational Physics10.1016/j.jcp.2023.112696498:COnline publication date: 1-Feb-2024
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Bourgeois RTremblin PKokh SPadioleau T(2024)Recasting an operator splitting solver into a standard finite volume flux-based algorithm. The case of a Lagrange-projection-type method for gas dynamicsJournal of Computational Physics10.1016/j.jcp.2023.112594496:COnline publication date: 27-Feb-2024
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Kemm F(2024)New options for explicit all Mach number schemes by suitable choice of time integration methodsJournal of Computational Physics10.1016/j.jcp.2023.112583496:COnline publication date: 27-Feb-2024
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Jung JPerrier V(2022)Steady low Mach number flowsJournal of Computational Physics10.1016/j.jcp.2022.111462468:COnline publication date: 1-Nov-2022
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