High-Order Asymptotic-Preserving IMEX schemes for an ES-BGK model for Gas Mixtures

TL;DR

This paper develops a high-order, explicit, asymptotic-preserving IMEX scheme for the multi-species ES-BGK gas mixture model, ensuring stability, accuracy, and correct asymptotics across regimes.

Contribution

It extends IMEX schemes to multi-species ES-BGK models, providing a fully explicit, high-order, stable solver that handles multiple species and preserves asymptotic limits.

Findings

Numerical verification of AP property across regimes.

High-order accuracy demonstrated in multidimensional tests.

Stable and efficient handling of multiple gas species.

Abstract

In this work we construct a high-order Asymptotic-Preserving (AP) Implicit-Explicit (IMEX) scheme for the ES-BGK model for gas mixtures introduced in [Brull, Commun. Math. Sci., 2015]. The time discretization is based on the IMEX strategy proposed in [Filbet, Jin, J. Sci. Comput., 2011] for the single-species BGK model and is here extended to the multi-species ES-BGK setting. The resulting method is fully explicit, uniformly stable with respect to the Knudsen number and, in the fluid regime, it reduces to a consistent and high-order accurate solver for the limiting macroscopic equations of the mixture. The IMEX structure removes the stiffness associated with the relaxation term so that the time step is constrained only by a hyperbolic CFL condition. The full solver couples a high-order space and velocity discretization that includes third-order time integration, a CWENO3 finite-volume reconstruction in space, exact conservation of macroscopic moments in the discrete velocity space, and a multithreaded implementation. The proposed approach can handle an arbitrary number of species. Its accuracy and robustness are demonstrated on a set of multidimensional kinetic tests for gas mixtures, where the AP property and the correct asymptotics are numerically verified across different regimes.