A low Mach number asymptotic analysis of dissipation-reducing methods for curing shock instability  

作　　者：Hongping GUO Xun WANG Zhijun SHEN 

机构地区：[1]National Key Laboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics,Beijing,100088,China [2]Faculty of Mathematics,Baotou Teachers’College,Baotou,Inner Mongolia Autonomous Region,014030,China [3]School of Mathematical Sciences,Peking University,Beijing,100871,China [4]PKU-Changsha Institute for Computing and Digital Economy,Changsha,410205,China [5]Center for Applied Physics and Technology,Peking University,Beijing,100871,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2025年第4期723-744,共22页应用数学和力学(英文版)

基　　金：Project supported by the National Natural Science Foundation of China(Nos.12471367 and12361076);the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Nos.NJZY19186,NJZY22036,and NJZY23003)。

摘　　要：We are intrigued by the issues of shock instability,with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it.For a specific class of planar flow fields where the transverse direction exhibits vanishing but non-zero velocity components,such as a disturbed onedimensional(1D)steady shock wave,we conduct a formal asymptotic analysis for the Euler system and associated numerical methods.This analysis aims to illustrate the discrepancies among various low-dissipative numerical algorithms.Furthermore,a numerical stability analysis of steady shock is undertaken to identify the key factors underlying shock-stable algorithms.To verify the stability mechanism,a consistent,low-dissipation,and shock-stable HLLC-type Riemann solver is presented.

关 键 词：Riemann solver numerical shock instability low Mach number HLLC 

分 类 号：O354[理学—流体力学]