Validation of SUPG finite element simulations of shockwave/turbulent boundary layer interactions in hypersonic flows

This paper assesses the validity of a stabilized finite element formulation applied to shockwave/turbulent boundary layer interaction (SWTBLI) problems. Our focus is on comparison with two well-defined experimental data sets to evaluate the performance of the Spalart-Allmaras turbulence model. The streamline-upwind Petrov/Galerkin finite element formulation and the fully implicit numerical treatment of the turbulence model is first presented. We choose for validation two experiments which differ in the mechanism through which the SWTBLI is created. The first case is that of high Mach number flow over a compression ramp, and the second is an externally-generated shockwave of varying strength impinging on a turbulent flat plate boundary layer. A particularly unique aspect of our numerical implementation is that it has been previously verified using the Method of Manufactured Solutions, hence we are confident that in this validation step that the selected mathematical models are implemented correctly. The combination of a verified numerical implementation, along with careful consideration of mesh and iterative convergence, allow us to critically assess validity of the underlying mathematical models.