Central upwind scheme based immersed boundary method for compressible flows around complex geometries

Abstract

The present work combines easy to implement high resolution central upwind scheme (CUS) with a ghost cell based discrete forcing immersed boundary method (IBM) and proposes a novel CUS-IBM finite volume solver to simulate high-speed compressible inviscid/viscous flows around complex geometries on Cartesian grids. Proposed CUS-IBM solver has been tested for a variety of inviscid and viscous compressible flow problems, ranging from transonic to supersonic flow speeds (0.625 < M < 3), involving flow over different geometries, i.e., bump, airfoil and cylinder. Results from our computations clearly show that solutions computed with the proposed method are in good agreement with the numerical data available in literature for the various inviscid/viscous and external/internal compressible flow problems. The present study demonstrates that the proposed CUS-IBM exhibits nominal second-order accuracy in space and is an easy to implement, robust and promising alternative to the methods involving Riemann solver and characteristics decomposition.