Characteristic based volume penalization method for numerical simulation of compressible flows on unstructured meshes

A characteristic based volume penalization method for numerical simulation of viscous compressible gas flows near solid bodies with immersed boundaries is presented. In contrast to other immersed boundary methods based on penalty functions, characteristic penalty functions ensure the correct formulation of the Neumann condition and, specifically, the adiabatic condition on the body surface. A numerical algorithm based on the method is described in detail. The algorithm combines the finite-volume approach based on high-order accurate EBR schemes in the outer flow region and first-order finite-difference schemes within the body. The developed algorithm can be used on meshes of arbitrary structure, including fully unstructured ones. The efficiency of the characteristic based volume penalization method and its implementation is demonstrated as applied to benchmark problems, such as the reflection of a shock wave and an acoustic pulse from a solid wall and the Couette flow. The solutions of the same problems produced by the well-known Brinkman penalization method are given for comparison.