Physics-based r-adaptive algorithms for high-speed flows and plasma simulations
Firas Ben Ameur, Andrea Lani
TL;DR
This work tackles the need for accurate yet efficient mesh adaptation in challenging high-speed and space-plasma flows by introducing a physics-driven r-adaptive framework. It develops a family of spring-based mesh-motion models (linear, torsional, semi-torsional, and ortho-semi-torsional) that reposition nodes according to flow monitors while preserving connectivity and parallel scalability in unstructured grids. Two auxiliary tools are proposed: a Mesh Quality Indicator (MQI) to assess adapted mesh quality and a Refinement Stop Indicator (RSI) to automate termination of refinement, both demonstrated across 2D and 3D test cases such as wedge flows, double cones, Hornung cylinders, hemispheres, solar wind–magnetosphere interactions, and MHD rotor. The results show improved shock resolution and feature capture with reduced element counts, along with practical guidance for parameter choices and tolerance settings, making the approach broadly applicable to hypersonic and plasma simulations.
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.