Local Discrete Velocity Grids for Multi-Species Rarefied Flow Simulations (Communications in Computational Physics, 2020)
This article deals with the derivation of an adaptive numerical method formono-dimensional kinetic equations for gas mixtures. For classical deterministic kinetic methods, the velocity domain is chosen accordingly to the initial condition. Insuch methods, this velocity domain is the same for all time, all space points and allspecies. The idea developed in this article relies on defining velocity domains thatdepend on space, time and species. This allows the method to locally adapt to thesupport of the distribution functions. The method consists in computing macroscopicquantities by the use of conservation laws, which enables the definition of such localgrids. Then, an interpolation procedure along with a upwind scheme is performed inorder to treat the advection term, and an implicit treatment of the BGK operator allowsfor the derivation of an AP scheme, where the stability condition is independent of therelaxation rate. The method is then applied to a series of test cases and compared to theclassical DVM method.