ECCOMAS 2024

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

  • Lodares, Diego (ETSIAE-UPM - School of Aeronautics)
  • Manzanero, Juan (ETSIAE-UPM - School of Aeronautics)
  • Ferrer, Esteban (ETSIAE-UPM - School of Aeronautics)
  • Valero, Eusebio (ETSIAE-UPM - School of Aeronautics)

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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 and 3D geometries using the RANS equations and the Spalart-Allmaras one-equation turbulence model. With the aim of replicating an industrial scenario, solid bodies are represented by triangular meshes. Finally, we propose a methodology to integrate the aerodynamic forces and moments generated by these bodies, which is direct when employing body-fitted meshes but requires special care with IBM. 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.