A Coupled IMEX Domain Decomposition Method for High-Order Time Integration of the ES-BGK Model of the Boltzmann Equation

TL;DR

This paper introduces a high-order domain decomposition method for the ES-BGK model of the Boltzmann equation, dynamically switching between fluid and kinetic models to improve accuracy and efficiency.

Contribution

It develops a coupled IMEX domain decomposition strategy that maintains high-order accuracy while efficiently handling equilibrium and non-equilibrium regions.

Findings

The method achieves high-order temporal convergence.

Numerical simulations validate robustness and accuracy.

The approach improves computational efficiency in 2D simulations.

Abstract

In this paper, we propose a high-order domain decomposition method for the ES-BGK model of the Boltzmann equation, which dynamically detects regions of equilibrium and non-equilibrium. Our implementation automatically switches between Euler equations in regions where the fluid is at equilibrium, and the ES-BGK model elsewhere. The main challenge addressed in this work is the development of a coupled strategy between the macroscopic and the kinetic solvers, which preserves the overall temporal order of accuracy of the scheme. A coupled IMEX method is introduced across decomposed subdomains and solvers. This approach is based on a coupled IMEX method and allows high accuracy and computational efficiency. Several numerical simulations in two space dimensions are performed, in order to validate the robustness of our approach and the expected temporal high-order convergence.