Progress in the development of an immersed boundary viscous wall-model for 3d and high-speed flows

The excessive computational requirements for DNS and wall-resolved large eddy simulation (LES) make these methods intractable for simulations concerning flows over complex, real-world geometries. Wall-modeled LES (WMLES) approaches seek to reduce this cost by applying wall-layer models to turbulent boundary layers. Immersed boundary methods (IBMs) have grown in popularity over the past few decades due to the fact that the mesh can be automatically generated for any complex geometry-a potentially major advancement for common industrial CFD simulations. However, immersed boundary approaches suffer from reduced numerical stability at the wall, primarily attributable to irregular discretization of boundary operators. This is a problem that is especially significant in high Mach number WMLES, where numerical schemes must be both stable at high wavenum-bers and non-dissipative, which are conflicting requirements. This study aims to improve existing immersed boundary approaches as applied to WMLES of high speed flows. This is done by carefully addressing dissipation both away from and close to the wall, by using a locally-stabilized discretization approach, and by modifying the application of boundary conditions. Test cases presented here include a turbulent channel for basic validation, a hypersonic transitional boundary layer to investigate high-speed, zero-pressure-gradient flows, a hypersonic shock wave boundary layer interaction to investigate adverse pressure gradients, separation, and turbulent heating, and a hypersonic compression ramp which is significantly challenging as it combines all of the features from the aforementioned high-speed flow problems.