Immersed boundary methods for high-order discretization of the compressible Reynolds Averaged Navier-Stokes equations

Abstract

The Immersed Boundary Method (IBM) presents clear advantages for CFD simu lation of compressible ows around complex geometries. In contrast to the standard body- tted approach, in which meshes are designed to conform to geometries, the IBM treats solid obsta cles via local modi cation of the governing equations. Popular modi cations rest on adding volumetric penalization terms to those mesh cells that are covered by immersed bodies [1] or on imposing special boundary conditions on mesh faces surrounding them [2]. In the context of the nodal Discontinuous Galerkin Spectral Element Method (DGSEM), one can also apply subcell based limiting strategies to further discretize the immersed mesh cells employing a compatible low-order method [3]. In this paper, we present a comparison between these three techniques in a high-order setting to solve compressible ows around 2D geometries using the RANS equations with the Spalart-Allmaras one-equation turbulence model. Our results show that introducing wall model-based terms is necessary for IBM formulations to yield correct RANS ow elds, and suggest that subcell-based limiting in the context of IBM can be advantageous in terms of convergence while maintaining solution accuracy.

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