Assessment of volume penalization and immersed boundary methods for compressible flows with various thermal boundary conditions

Abstract

A continuous forcing immersed boundary method (IBM) and a volume penalization method are investigated to simulate compressible viscous flows past an isothermal or adiabatic solid obstacle using a body non-conformal Cartesian grid. The present methods are validated on a large range of flow configurations such as incompressible and compressible flows (steady or unsteady) past isothermal or adiabatic solid obstacles. An adiabatic condition with implicit treatment of the source term is derived for the penalization method, taking advantage of the framework of the ghost-cell methods. Accuracy and computational cost of the methods are discussed. Three-dimensional supersonic flow configurations are carried out with the penalization method. The coupling between the porosity parameter and the different boundary conditions of the present penalization method is investigated in order to properly reproduce the wave reflection on a solid wall. Finally, a new penalization model is designed to improve the shock wave reflection on a solid surface while significantly reducing the computational cost compared to the previous porosity model.