Immersed boundary methods for high-order discretization of the compressible Reynolds Averaged Navier-Stokes equations
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The Immersed Boundary Method (IBM) presents clear advantages for CFD simulation of compressible flows around complex geometries. In contrast to the standard body-fitted approach, in which meshes are designed to conform to geometries, the IBM treats solid obstacles via local modification of the governing equations. Popular modifications 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 flows around 2D geometries using the RANS equations and 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 flow fields, and suggest that subcell-based limiting in the context of IBM can be advantageous in terms of convergence while maintaining solution accuracy. REFERENCES [1] J. Kou, S. Joshi, A. Hurtado-de-Mendoza, K. Puri, C. Hirsch, E. Ferrer, Immersed boundary method for high-order flux reconstruction based on volume penalization, Journal of Computational Physics, Volume 448, 110721, 2022 (available online). [2] Péron, S., Benoit, C., Renaud, T. et al. An immersed boundary method on Cartesian adaptive grids for the simulation of compressible flows around arbitrary geometries. Engineering with Computers 37, 2419–2437, 2021. [3] Rueda-Ramírez, A., Pazner, W, and Gassner, G. (2022). Subcell limiting strategies for discontinuous Galerkin spectral element methods. Computers & Fluids, Volume 247, 105627, 2022.