Robin Based Semi-Implicit Coupling in Fluid-Structure Interaction: Stability Analysis and Numerics

Matteo Astorino 1 Franz Chouly 1 Miguel Angel Fernández 1, *
* Corresponding author
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 report, we propose a semi-implicit coupling scheme for the numerical simulation of fluid-structure interaction systems involving a viscous incompressible fluid. The scheme is stable irrespectively of the so-called added-mass effect and allows for conservative time-stepping within the structure. The efficiency of the scheme is based on the explicit splitting of the viscous effects and geometrical/convective non-linearities, through the use of the Chorin-Temam projection scheme within the fluid. Stability comes from the implicit pressure-solid coupling and a specific Robin treatment of the explicit viscous-solid coupling, derived from Nitsche's method.
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Matteo Astorino, Franz Chouly, Miguel Angel Fernández. Robin Based Semi-Implicit Coupling in Fluid-Structure Interaction: Stability Analysis and Numerics. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2009, 31 (6), pp.4041-4065. ⟨10.1137/090749694⟩. ⟨inria-00361284v2⟩

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