首页|An Arbitrarily High Order and Asymptotic Preserving Kinetic Scheme in Compressible Fluid Dynamic
An Arbitrarily High Order and Asymptotic Preserving Kinetic Scheme in Compressible Fluid Dynamic
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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 multi-dimensional systems.We have assessed our method on several problems for two-dimen-sional 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.
Kinetic schemeCompressible fluid dynamicsHigh order methodsExplicit schemesAsymptotic preservingDefect correction method
Rémi Abgrall、Fatemeh Nassajian Mojarrad
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Institute of Mathematics,University of Zürich,Winterthurerstrasse 190,CH 8057 Zürich,Switzerland
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