A sharp-interface immersed boundary method for moving objects in compressible viscous flows

Abstract

Sharp-interface Immersed Boundary Methods for moving solids in compressible viscous flows often exhibit spurious noise propagating from the moving boundary. In compressible flows, filtering or upwinding discretization techniques are often used to overcome the problem. In the present work, we show that using a conservative energy-preserving finite difference method for convection in combination with a Ghost-Point-Forcing-Method (GPFM) is able to keep controlled the pressure-velocity spurious noise. In order to deal with compressible flow in a wide range of Mach numbers the shock-dynamics appearing in high-speed flows conditions has been addressed hybridising the latter scheme with a fifth-order weighted-essentially-non-oscillatory (WENO) scheme. The latter, in the path of keeping the numerical dissipation minimal, has been confined around the shock locations using a proper detector. In this respect, the method appears a suitable alternative for direct and large-eddy simulation of moving objects in compressible flows. The entire methodology was found to be robust ranging from weakly compressible to highly supersonic flows including shocks. In order to prove the cleanliness and the robustness of the method, several well-documented benchmarks and test cases, in a wide range of both Reynolds and Mach numbers, are presented.