The Effect of Upwinding on High-Order Shock-Fitting Schemes
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Shock-fitting is a method to solve moving shock problems with high-order accuracy. Upwind stabilization is commonly used for mesh movement in oblique shock problems, but the effects on the solution are weakly understood. Here, the compressible Euler equations are solved using hp-FEM with a moving mesh. The scheme is analyzed using a von Neumann analysis to quantify the effects of upwind stabilization applied to the equation of mesh movement. For validation, eigenvalues from the analysis are compared to results from the FEM solutions. Test cases are presented with varying Mach numbers, flow angles, and wavenumbers to demonstrate how upwind stabilization changes the eigenvalues. The results indicate that upwind stabilization is necessary for both normal and oblique shocks.
