Locally refined discrete velocity grids for stationary rarefied flow simulations

TL;DR

This paper introduces a method for automatically generating locally refined discrete velocity grids that significantly reduce memory requirements and computational cost for 3D rarefied flow simulations, maintaining accuracy.

Contribution

The authors propose a novel approach to create adaptive velocity grids tailored to specific simulations, improving efficiency over traditional Cartesian grids.

Findings

Reduced memory usage in 3D simulations

Maintained accuracy with fewer velocity points

Enabled practical hypersonic flow simulations

Abstract

Most of deterministic solvers for rarefied gas dynamics use discrete velocity (or discrete ordinate) approximations of the distribution function on a Cartesian grid. This grid must be sufficiently large and fine to describe the distribution functions at every space position in the computational domain. For 3-dimensional hypersonic flows, like in re-entry problems, this induces much too dense velocity grids that cannot be practically used, for memory storage requirements. In this article, we present an approach to generate automatically a locally refined velocity grid adapted to a given simulation. This grid contains much less points than a standard Cartesian grid and allows us to make realistic 3-dimensional simulations at a reduced cost, with a comparable accuracy.