Physics-based r-adaptive algorithms for high-speed flows and plasma simulations

TL;DR

This paper introduces a physics-based r-adaptive mesh algorithm for high-speed flow and plasma simulations, improving numerical accuracy by dynamically repositioning mesh nodes based on physical phenomena.

Contribution

It presents a novel mesh adaptation technique using physics-driven pseudo-elastic systems and introduces quality and stop indicators for automated refinement.

Findings

Enhanced mesh quality in high-speed flow simulations

Automatic mesh refinement driven by physical properties

Demonstrated applicability across various physical models

Abstract

The computational modeling of high-speed flows (e.g. hypersonic) and space plasmas is characterized by a plethora of complex physical phenomena, in particular involving strong oblique shocks, bow shocks and/or shock waves boundary layer interactions. The characterization of those flows requires accurate, robust and advanced numerical techniques. To this end, adaptive mesh algorithms provide an automatic way to improve the quality of the numerical results, by increasing the mesh density where required in order to resolve the most critical physical features. In this work, we propose a r-adaptive algorithm that consists in repositioning mesh nodes as resulting from the solution of a physics-driven pseudo-elastic system of equations. The developed mesh refinement techniques are based upon spring networks deriving from linear, semi-torsional and ortho-semi- torsional analogies, but driven by a combination of local physical and geometrical properties depending on a user-defined monitoring flow variable. Furthermore, a mesh quality indicator is developed within this work in order to grade and investigate the quality of an adapted mesh. Finally, a refinement stop indicator is proposed and demonstrated in order to further automatize the resulting adaptive simulation. All new physics-based mesh motion algorithms are illustrated through multiple examples that emphasize the applicability to different physical models and problems together with the improved quality of the results.