Local discrete velocity grids for deterministic rarefied flow simulations

TL;DR

This paper introduces a dynamic, local velocity grid approach for deterministic rarefied gas flow simulations, reducing computational costs by adapting to the distribution functions' width, demonstrated through 1D test cases.

Contribution

It proposes a novel adaptive local velocity grid method that improves efficiency over traditional global grids in rarefied flow simulations.

Findings

Reduces computational cost for high-speed flow simulations.

Demonstrates effectiveness through 1D test cases.

Highlights advantages and limitations of the local grid approach.

Abstract

Most of numerical methods for deterministic simulations of rarefied gas flows use the discrete velocity (or discrete ordinate) approximation. In this approach, the kinetic equation is approximated with a global velocity grid. The grid must be large and fine enough to capture all the distribution functions, which is very expensive for high speed flows (like in hypersonic aerodynamics). In this article, we propose to use instead different velocity grids that are local in time and space: these grids dynamically adapt to the width of the distribution functions. The advantages and drawbacks of the method are illustrated in several 1D test cases.