R-adaptive algorithms for high-speed flows and plasma simulations

Abstract

The computational modeling of high-speed flows (e.g. hypersonic) and space plasmas is characterized by plethora of complex physical phenomena, in particular involving strong bow shocks and/or shock waves boundary layer interactions. The characterization of those flows requires accurate, robust, advanced numerical techniques and well tailored computational meshes for resolving all features of interest. 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 novel spring analogies deriving from linear, semi-torsional and ortho-semi-torsional analogies, but driven by a combination of local physical and geometric properties depending on a user-defined monitoring flow variable. All new mesh motion algorithms are illustrated through multiple examples that emphasize the applicability to different flow/plasma applications and problems together with the improved quality of the results.