A Hierarchy of Hybrid Numerical Methods for Multi-Scale Kinetic Equations

TL;DR

This paper develops a hierarchy of hybrid numerical methods for multi-scale kinetic equations, leveraging moment realizability matrices to adaptively combine different fluid models like Euler, Navier-Stokes, and higher-order systems.

Contribution

It introduces a new hierarchy of hybrid schemes based on moment realizability matrices, enabling flexible coupling of various fluid models for kinetic equations.

Findings

Flexible hybrid schemes for multi-scale kinetic equations.

Inclusion of higher-order models like Burnett systems.

Framework adaptable to different fluid dynamics models.

Abstract

In this paper, we construct a hierarchy of hybrid numerical methods for multi-scale kinetic equations based on moment realizability matrices, a concept introduced by Levermore, Morokoff and Nadiga. Following such a criterion, one can consider hybrid scheme where the hydrodynamic part is given either by the compressible Euler or Navier-Stokes equations, or even with more general models, such as the Burnett or super-Burnett systems.