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

作　　者：Yanqun Jiang Xun Chen Xu Zhang Tao Xiong Shuguang Zhou 

机构地区：[1]Department of Mathematics,Southwest University of Science and Technology,621010 Mianyang,China [2]School of Mathematical Sciences,Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing,Xiamen University,361005 Xiamen,China [3]Computational Aerodynamics Institute,China Aerodynamics Research and Development Center,621000 Mianyang,China

出　　处：《Advances in Aerodynamics》2020年第1期555-578,共24页空气动力学进展（英文）

基　　金：the National Numerical Wind Tunnel Project(No.NNW2018-ZT4A08);the National Natural Science Foundation of China(Nos.11872323 and 11971025);the Natural Science Foundation of Fujian Province(No.2019J06002)。

摘　　要：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.

关 键 词：High order scheme IMEX time discretization WCNS Asymptotic-preserving property Low Mach number Isentropic Euler equations 

分 类 号：O17[理学—数学]