High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

Advances in Aerodynamics

Shuguang Zhou¹  Xun Chen²  Xu Zhang²  Yanqun Jiang²  Tao Xiong³ 

[1] Computational Aerodynamics Institute, China Aerodynamics Research and Development Center;Department of Mathematics, Southwest University of Science and Technology;School of Mathematical Sciences, Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University;

关键词: High order scheme;    IMEX time discretization;    WCNS;    Asymptotic-preserving property;    Low Mach number;    Isentropic Euler equations;   

DOI  :  10.1186/s42774-020-00052-9

来源: DOAJ

【 摘 要 】

Abstract The computation of compressible flows at all Mach numbers is a very challenging problem. An efficient numerical method for solving this problem needs to have shock-capturing capability in the high Mach number regime, while it can deal with stiffness and accuracy in the low Mach number regime. This paper designs a high order semi-implicit weighted compact nonlinear scheme (WCNS) for the all-Mach isentropic Euler system of compressible gas dynamics. To avoid severe Courant-Friedrichs-Levy (CFL) restrictions for low Mach flows, the nonlinear fluxes in the Euler equations are split into stiff and non-stiff components. A third-order implicit-explicit (IMEX) method is used for the time discretization of the split components and a fifth-order WCNS is used for the spatial discretization of flux derivatives. The high order IMEX method is asymptotic preserving and asymptotically accurate in the zero Mach number limit. One- and two-dimensional numerical examples in both compressible and incompressible regimes are given to demonstrate the advantages of the designed IMEX WCNS.

【 授权许可】

Unknown