Direct Simulation Monte Carlo Methods for Hypersonic Flows with Automatic Mesh Optimization

Abstract

High-Altitude Low-Orbit 3D (HALO3D) is a comprehensive multidisciplinary software system being developed by the current authors to simulate flowfields around hypersonic aircraft whose flightpath spans low (continuum) to high (rarefied) altitudes. This paper presents a methodology for coupling HALO3D’s particle-based rarefied flow module, HALO3D–Direct Simulation Monte Carlo (HALO3D-DSMC), with a solution-driven edge-based automatic mesh optimization algorithm, OptiGrid. The paper studies the choice of optimization scalars and constraints for DSMC solvers, an aspect believed to be currently lacking in the literature. Three optimization constraints are used: minimum and maximum edge lengths and a target number of nodes/cells. Mesh optimization is conducted for Bird’s leading-edge case and flows over two- and three-dimensional cylinder geometries for freestream Knudsen numbers ranging from 0.01 to 0.047. An adaptation scalar set combining flow variables such as density, velocity components, modal temperatures, pressure, and Mach number produces an unstructured collisional-sampling mesh that greatly improves the quality of the solution without necessarily increasing mesh size. The solutions represented by the optimal meshes are smooth and free of irregularities, with salient flow features being captured well. In addition, the coupled system can simulate complex geometries and multiscale flow features with arbitrarily generated initial grids.