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Generalized Brinkman Volume Penalization Method for Compressible Flows Around Moving Obstacles

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Abstract

A Galilean-invariant generalization of the Brinkman volume penalization method (BVPM) for compressible flows, which extends the applicability of the method to problems of the flow around moving obstacles, is proposed. 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 BVPM for compressible flows around moving obstacles is demonstrated for a number of test problems of the direct reflection of a one-dimensional acoustic pulse from a stationary and moving plane surface, scattering of an acoustic wave by a stationary cylinder, and the subsonic flow of a viscous gas around an oscillating cylinder. The numerical results agree closely with the reference solutions and theoretical estimates of the convergence of the method and they confirm the invariance of the proposed formulation with respect to the Galilean transformations.

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ACKNOWLEDGMENTS

The results were obtained using the equipment of the Center for Shared Use, Keldysh Institute of Applied Mathematics, Russian Academy of Sciences (http://ckp.kiam.ru).

Funding

This work was supported by the Russian Science Foundation, project 20-41-09018.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    N. S. Zhdanova, I. V. Abalakin & O. V. Vasilyev

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  1. N. S. Zhdanova
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  2. I. V. Abalakin
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  3. O. V. Vasilyev
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Correspondence to N. S. Zhdanova or O. V. Vasilyev.

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Zhdanova, N.S., Abalakin, I.V. & Vasilyev, O.V. Generalized Brinkman Volume Penalization Method for Compressible Flows Around Moving Obstacles. Math Models Comput Simul 14, 716–726 (2022). https://doi.org/10.1134/S2070048222050180

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