Geodesic
Generalized Brinkman volume penalization method for compressible flows around moving obstacles
Matematičeskoe modelirovanie, Tome 34 (2022) no. 2, pp. 41-57.

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This work presents a Galilean-invariant generalization of the Brinkman volume penalization method for compressible flows, which extends the applicability of the method to problems with moving obstacles. The developed method makes it possible to carry out simulations on non-body fitted meshes of arbitrary structure, including completely unstructured computational grids. The efficiency of the Galilean-invariant generalization of the Brinkman volume penalization method for compressible flows around moving obstacles is demonstrated for a number of benchmark flows such as one-dimensional acoustic pulse reflection from a plane stationary and moving surface, the 2-D acoustic scattering by the cylinder generated by localized acoustic source, and subsonic viscous flow around an oscillating cylinder. The numerical results agree well with the reference solutions, theoretical estimates of the convergence of the method, and confirm the Galilean invariance of the proposed formulation.
Keywords: unstructured meshes, immersed boundary method, volume penalization method, fictitious domain method, flow around moving obstacles. 
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N. S. Zhdanova; I. V. Abalakin; O. V. Vasilyev. Generalized Brinkman volume penalization method for compressible flows around moving obstacles. Matematičeskoe modelirovanie, Tome 34 (2022) no. 2, pp. 41-57. http://geodesic.mathdoc.fr/item/MM_2022_34_2_a3/

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