  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.
