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Convergence analysis of a penalization method for the three-dimensional motion of a rigid body in an incompressible viscous fluid

Claire Bost 1 Georges-Henri Cottet 1, * Emmanuel Maitre 1 
* Corresponding author
1 EDP - Equations aux Dérivées Partielles
LJK - Laboratoire Jean Kuntzmann
Abstract : We present and analyze a penalization method wich extends the the method of [1] to the case of a rigid body moving freely in an incompressible fluid. The fluid-solid system is viewed as a single variable density flow with an interface captured by a level set method. The solid velocity is computed by averaging at avery time the flow velocity in the solid phase. This velocity is used to penalize the flow velocity at the fluid-solid interface and to move the interface. Numerical illustrations are provided to illustrate our convergence result. A discussion of our result in the light of existing existence results is also given.
[1] Ph. Angot, C.-H. Bruneau and P. Fabrie, A penalization method to take into account obstacles in incompressible viscous flows, Numer. Math. 81: 497--520 (1999)
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Submitted on : Monday, July 12, 2010 - 2:23:04 PM
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Claire Bost, Georges-Henri Cottet, Emmanuel Maitre. Convergence analysis of a penalization method for the three-dimensional motion of a rigid body in an incompressible viscous fluid. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2010, 48 (4), pp.1313-1337. ⟨10.1137/090767856⟩. ⟨hal-00352808v2⟩

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