An Improved Characteristic Based Volume Penalization Method for the Euler Equations Towards Icing Applications

Abstract Immersed boundary methods (IBMs) are an interesting alternative to the usual body-fitted mesh approach when dealing with complex geometries as they allow simpler mesh generation. The volume penalization method (an IBM) is commonly used for incompressible and compressible viscous flows but only one application to compressible inviscid flows can be found, which uses the characteristic-based volume penalization (CBVP) method. This approach penalizes the Euler equations to enforce a no-penetration velocity and an adiabatic wall while accounting for wall curvature. A new penalization method based on the CBVP is proposed to impose the conservation of entropy and total enthalpy in the normal direction to the wall instead of the classical adiabatic condition. The two approaches are compared and numerically tested on several cases: weakly compressible flow around a circular cylinder, subsonic flow around a NACA0012 airfoil and flow around a challenging high curvature ice horn. The new method is found to be more accurate than the CBVP on coarser meshes and better at retrieving attached flows for curved geometries. The paper concludes that the proposed method is suitable for general aerospace applications and beneficial for icing simulations which can exhibit highly curved geometries.