Towards a viscous wall model for immersed boundary methods

Immersed boundary methods have drawn wide attention over the past decades due to the fact that the mesh generation process can be automated independent of the complexity of the geometry. While many immersed boundary approaches have been developed, there remains one key challenge that has yet to be solved. The primary shortcoming of Cartesian mesh immersed boundary methods is the inability of efficiently resolving thin turbulent boundary layers encountered in high-Reynolds number flow applications. The inefficiency of resolving this thin region of the flow is associated with the use of constant aspect ratio Cartesian grid cells. Conventional CFD approaches can efficiently resolve the large wall-normal gradients by employing grid stretching towards the wall thereby creating large aspect ratio cells near the wall. This paper discusses different types of local wall modeling approaches that were proposed in previous research studies and combines them with an immersed boundary method. Standard subsonic turbulence modeling test cases, i.e., flow past the NACA0012 airfoil and flow over a bump in a channel, are used to test different implementations. A key focus of this paper is to investigate the limitations of the different wall models, numerical implementation details of the immersed boundary method and the coupling effects.