A sharp interface immersed boundary method for thin-walled geometries in viscous compressible flows

Compressible flows at low Mach numbers are prevalent in various engineering applications, such as combustion, aeroacoustics, heat transfer, and more. In this study, we present a sharp interface immersed boundary method (IBM) tailored for low Mach number viscous compressible flows. The IBM is developed using a robust interpolation scheme, ensuring stability for complex geometries with zero-thickness walls. To satisfy the boundary condition, the interpolation needs to use points from the same side, thus preventing interaction across the zero-thickness wall. Additionally, a simple modification is proposed to fully eliminate interaction between two opposite sides when performing stencil calculations for high order schemes. This is achieved by gradually reducing the order when the stencil is close to the wall. Furthermore, the IBM efficiently addresses the issue of moving objects in compressible flows, specifically the treatment of fresh cells, without necessitating any special treatment. Results showcase the method's applicability to aerodynamic simulations at low Mach numbers, simulations of compression and expansion processes, and direct numerical simulations of aeroacoustics.