A multiscale discrete velocity method for model kinetic equations

TL;DR

This paper introduces a multiscale discrete velocity method that improves traditional schemes by reducing numerical dissipation and accurately modeling gas flows across all regimes, from free molecules to continuum flows.

Contribution

The paper presents a novel multiscale DVM that splits fluxes into equilibrium and nonequilibrium parts, enhancing accuracy in continuum regimes compared to existing methods.

Findings

Accurately models gas flows in all regimes from free molecule to continuum.

Reduces numerical dissipation in continuum flow simulations.

Demonstrates good performance through various test cases.

Abstract

In this paper, authors focus effort on improving the conventional discrete velocity method (DVM) into a multiscale scheme in finite volume framework for gas flow in all flow regimes. Unlike the typical multiscale kinetic methods unified gas-kinetic scheme (UGKS) and discrete unified gas-kinetic scheme (DUGKS), which concentrate on the evolution of the distribution function at the cell interface, in the present scheme the flux for macroscopic variables is split into the equilibrium part and the nonequilibrium part, and the nonequilibrium flux is calculated by integrating the discrete distribution function at the cell center, which overcomes the excess numerical dissipation of the conventional DVM in the continuum flow regime. Afterwards, the macroscopic variables are finally updated by simply integrating the discrete distribution function at the cell center, or by a blend of the increments based on the macroscopic and the microscopic systems, and the multiscale property is achieved. Several test cases, involving unsteady, steady, high speed, low speed gas flows in all flow regimes, have been performed, demonstrating the good performance of the multiscale DVM from free molecule to continuum Navier-Stokes solutions and the multiscale property of the scheme is proved.