A novel stabilization method for high-order shock fitting with finite element methods

A moving-grid, shock-fitting, finite element method has been implemented that can achieve high-order accuracy for flow simulations with shocks. In this approach, edges in the computational mesh are fitted to shock front and moved throughout simulation. The Euler or Navier-Stokes equations solved on moving an arbitrary Lagrangian-Eulerian framework. is two-dimensions context of a streamwise upwind Petrov-Galerkin discretization unstructured triangular meshes adaptation. It shown interface motion equation wave nature, disturbances propagate along interface. SUPG stabilization term introduced critical ensuring do not lead non-convergent solution behavior. formal order scheme verified, performance proposed assessed both inviscid viscous problems. was found present predicts smooth noise-free surface heating hypersonic over cylinder purely irregular elements.