(untitled) (Communications in Computational Physics, 2020)
This article deals with the derivation of an adaptive numerical method for mono-dimensional kinetic equations for gas mixtures. For classical deterministic kinetic methods, the velocity domain is chosen accordingly to the initial condition. In such methods, this velocity domain is the same for all time, all space points and all species. The idea developed in this article relies on defining velocity domains that depend on space, time and species. This allows the method to locally adapt to the support of the distribution functions. The method consists in computing macroscopic quantities by the use of conservation laws, which enables the definition of such local grids. Then, an interpolation procedure along with a upwind scheme is performed in order to treat the advection term, and an implicit treatment of the BGK operator allows for the derivation of an AP scheme, where the stability condition is independent of the relaxation rate. The method is then applied to a series of test cases and compared to the classical DVM method.