A hybrid moment method for multi-scale kinetic equations based on maximum entropy principle

TL;DR

This paper introduces a hybrid moment method that efficiently couples fluid and kinetic regimes in multi-scale kinetic equations using maximum entropy reconstruction, enabling unified numerical schemes and improved computational performance.

Contribution

It presents a novel hybrid approach combining regularized moments with maximum entropy principles for multi-scale kinetic equations, simplifying computations across regimes.

Findings

High efficiency demonstrated in numerical tests

Unified numerical scheme applicable to both regimes

Effective utilization of fluid region information

Abstract

We propose a hybrid moment method for the multi-scale kinetic equations in the framework of the regularized moment method [7]. In this method, the fourth order moment system is chosen as the governing equations in the fluid region. When transiting from the fluid regime to the kinetic regime, the maximum entropy principle is adopted to reconstruct the kinetic distribution function, so that the information in the fluid region can be utilized thoroughly. Moreover, only one uniform set of numerical scheme is needed for both the fluid and kinetic regions. Numerical tests show the high efficiency of this new hybrid method.