Implicit Update of the Moment Equations for a Multi-Species, Homogeneous BGK Model

Abstract: A simple iterative approach for solving a set of implicit kinetic moment equations is proposed. This implicit solve is a key component in the IMEX discretization of the multi-species Bhatnagar-Gross-Krook (M-BGK) model with nontrivial collision frequencies depending on individual species temperatures. We prove that under mild time step restrictions, the iterative method generates a contraction mapping. Numerical simulations are provided to illustrate results of the IMEX scheme using the implicit moment solver.