Truly multi-dimensional all-speed schemes for the Euler equations on Cartesian grids

JOURNAL OF COMPUTATIONAL PHYSICS

卷:435

Article

Barsukow, Wasilij¹ 

[1] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

关键词: Low Mach number;    Euler equations;    Lagrange projection;    Relaxation solver;    Multi-dimensional methods;   

DOI  :  10.1016/j.jcp.2021.110216

来源: Elsevier

【 摘 要 】

Finite volume schemes often have difficulties to resolve the low Mach number (incompressible) limit of the Euler equations. Incompressibility is only non-trivial in multiple spatial dimensions. Low Mach fixes, however generally are applied to the onedimensional method and the method is then used in a dimensionally split way. This often reduces its stability. Here, it is suggested to keep the one-dimensional method as it is, and only to extend it to multiple dimensions in a particular, all-speed way. This strategy is found to lead to much more stable numerical methods. Apart from the conceptually pleasing property of modifying the scheme only when it becomes necessary, the multidimensional all-speed extension also does not include any free parameters or arbitrary functions, which generally are difficult to choose, or might be problem dependent. The strategy is exemplified on a Lagrange Projection method and on a relaxation solver. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free