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

TL;DR

This paper introduces an iterative implicit solver for kinetic moment equations in a multi-species BGK model, enabling efficient IMEX discretization with proven convergence under certain conditions.

Contribution

It presents a novel iterative method for implicit moment equations in multi-species BGK models, improving computational efficiency and stability.

Findings

The iterative method converges under mild time step restrictions.

Numerical simulations demonstrate the effectiveness of the IMEX scheme.

The approach handles nontrivial collision frequencies depending on species temperatures.

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.