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Explicit coupling schemes for a fluid-fluid interaction problem arising in hemodynamics

Miguel Angel Fernández 1 Jean-Frédéric Gerbeau 1 Saverio Smaldone 1
1 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
Abstract : In this work we propose a new approach to the loosely coupled time-marching of a fluid-fluid interaction problems involving the incompressible Navier-Stokes equations. The methods combine a specific explicit Robin-Robin treatment of the interface coupling with a weakly consistent interface pressure stabilization in time. A priori energy estimates guaranteeing stability of the splitting are obtained for a total pressure formulation of the coupled problem. The performance of the proposed schemes is illustrated on several numerical experiments related to simulation of aortic blood flow.
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https://hal.inria.fr/hal-00915213
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Miguel Angel Fernández, Jean-Frédéric Gerbeau, Saverio Smaldone. Explicit coupling schemes for a fluid-fluid interaction problem arising in hemodynamics. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2014, 36 (6), pp.2557-2583. ⟨10.1137/130948653⟩. ⟨hal-00915213v2⟩

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