An Arbitrarily High Order and Asymptotic Preserving Kinetic Scheme in Compressible Fluid Dynamic  

作　　者：Remi Abgrall Fatemeh Nassajian Mojarrad 

机构地区：[1]Institute of Mathematics,University of Zurich,Winterthurerstrasse 190,CH 8057 Zürich,Switzerland

出　　处：《Communications on Applied Mathematics and Computation》2024年第2期963-991,共29页应用数学与计算数学学报（英文）

基　　金：funded by the SNF project 200020_204917 entitled"Structure preserving and fast methods for hyperbolic systems of conservation laws".

摘　　要：We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics,both in time and space,which include the relaxation schemes by Jin and Xin.These methods can use the CFL number larger or equal to unity on regular Cartesian meshes for the multi-dimensional case.These kinetic models depend on a small parameter that can be seen as a"Knudsen"number.The method is asymptotic preserving in this Knudsen number.Also,the computational costs of the method are of the same order of a fully explicit scheme.This work is the extension of Abgrall et al.(2022)[3]to multidimensional systems.We have assessed our method on several problems for two-dimensional scalar problems and Euler equations and the scheme has proven to be robust and to achieve the theoretically predicted high order of accuracy on smooth solutions.

关 键 词：Kinetic scheme Compressible fluid dynamics High order methods Explicit schemes Asymptotic preserving Defect correction method 

分 类 号：O35[理学—流体力学]