Projection schemes for fluid flows through a porous interface

Alfonso Caiazzo 1, * Miguel Angel Fernández 1, * Jean-Frédéric Gerbeau 1, * Vincent Martin 2, *
* 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 : This paper presents a numerical method to simulate an incompressible fluid through an immersed porous interface. The interface is modeled by a surface measure term in the Navier-Stokes equations and it is characterized by a resistance parameter. This approach can be used for example to model valves or to simulate blood flood through an immersed stent. Starting from a monolithic formulation proposed recently, a fractional step algorithm is derived. The difficult point is that this formulation is singular when the resistance vanishes, which can be a serious issue in some applications. We show that an appropriate Nitsche's treatment of the interface condition fixes this problem and ensures uniform energy stability in time, for any non-negative value of the resistance. The theoretical stability and convergence results are illustrated with numerical experiments
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Alfonso Caiazzo, Miguel Angel Fernández, Jean-Frédéric Gerbeau, Vincent Martin. Projection schemes for fluid flows through a porous interface. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2011, 33 (2), pp.541-564. ⟨10.1137/100788124⟩. ⟨inria-00462103⟩

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