The Moving Discontinuous Galerkin Method with Interface Condition Enforcement (MDG-ICE) is a high-order method that weakly enforces conservation and interface conditions for accurate flow simulation. An optimization solver based on the Levenberg-Marquardt algorithm enhances robustness and prevents cell degeneration. MDG-ICE formulation applied to challenging test cases yields accurate, oscillation-free results. Anisotropic grid regularization inhibits grid motion in directions with small element length scales. The method adapts the grid to fit shocks and resolve smooth regions without artificial dissipation. The nonlinear solver incorporates increment limiting and adaptive, elementwise regularization to prevent cell degeneration. Results show successful resolution of viscous shocks with highly symmetric surface heat-flux profiles.
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