A kinetic transport-projection splitting algorithm for an hierarchy of moment closures of gas-kinetic equations

TL;DR

This paper introduces a transport-projection splitting algorithm for solving moment closure models of gas-kinetic equations, demonstrating convergence to classical solutions through a geometric approach.

Contribution

It presents a novel splitting scheme based on dual kinetic densities for constructing solutions to moment closure PDEs of gas-kinetic models.

Findings

Convergence of the scheme to unique classical solutions

Effective approximation of moment closure models

Utilization of geometric properties in scheme design

Abstract

We review some geometrical properties of models of moment closures of gas-kinetic equations, and consider a transport-projection splitting scheme for construction of solutions of such closures. The scheme, formulated in terms of a dual kinetic density, defines the kinetic density in successive superposition of transport in $x$--direction and projection to a finite dimensional linear space in a weighted $L^2$ space, in the kinetic variable $v.$ Given smooth initial data, we show that the approximate solutions converge to a unique classical solution of a system of moment closure PDEs.