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A penalization method to take into account obstacles in incompressible viscous flows

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Abstract.

From the Navier-Stokes/Brinkman model, a penalization method has been derived by several authors to compute incompressible Navier-Stokes equations around obstacles. In this paper, convergence theorems and error estimates are derived for two kinds of penalization. The first one corresponds to \(L^2\) penalization inducing a Darcy equation in the solid body, the second one corresponds to a \(H^1\) penalization and induces a Brinkman equation in the body. Numerical tests are performed to confirm the efficiency and accuracy of the method.

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Authors and Affiliations

  1. IRPHE, CNRS UMR 6594, Equipe Mathématiques Numériques pour la Modélisation, La Jetée – Technopôle de Château-Gombert, F-13451 Marseille, France , , , , , , FR

    Philippe Angot

  2. Mathématiques Appliquées de Bordeaux, CNRS et Université Bordeaux 1, 351, cours de la Libération, F-33405 Talence, France , , , , , , FR

    Charles-Henri Bruneau & Pierre Fabrie

Authors
  1. Philippe Angot
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  2. Charles-Henri Bruneau
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  3. Pierre Fabrie
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Received August 10, 1997

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Angot, P., Bruneau, CH. & Fabrie, P. A penalization method to take into account obstacles in incompressible viscous flows. Numer. Math. 81, 497–520 (1999). https://doi.org/10.1007/s002110050401

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  • DOI: https://doi.org/10.1007/s002110050401