An immersed boundary method for wall-modeled large-eddy simulation of turbulent high-Mach-number flows

Abstract

The excessive computational resource requirements for direct numerical simulation (DNS) and wall-resolved large eddy simulation (LES) make these methods intractable for simulations concerning turbulent flows over complex, real-world geometries. Wall-modeled LES (WMLES) approaches seek to reduce this cost by applying wall-layer models to the inner-most region of turbulent boundary layers. Immersed boundary methods (IBMs) have grown in popularity over the past few decades since 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 accuracy and, possibly, stability at the wall, primarily attributable to irregular discretization of boundary operators. This is a problem that is especially significant for WMLES of high Mach number flows, where numerical schemes have the conflicting requirements to be both stable at high wavenumbers and non-dissipative. This presentation introduces a coupled IBM-WMLES approach that is tailored to the simulation of high-speed turbulent flows. The basis of this method is to carefully address numerical dissipation and stability away from and close to the wall. This is achieved by using a hybrid central-upwind flux reconstruction scheme and careful application of smooth boundary conditions. The presented test cases evaluate the current scheme for a wide range of physical flow phenomena, and 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.