NDLI: Projection Schemes for Fluid Flows through a Porous Interface

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Fernndez, Miguel A. Martin, Vincent Caiazzo, Alfonso Gerbeau, Jean-Frdric
Copyright Year	2011
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 NavierStokes 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 treatment of the interface condition fixes this problem and ensures uniform energy stability in time for any nonnegative value of the resistance. The theoretical stability and convergence results are illustrated with numerical experiments.
Starting Page	541
Ending Page	564
Page Count	24
File Format	PDF
ISSN	10648275
DOI	10.1137/100788124
e-ISSN	10957197
Issue Number	2
Volume Number	33
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2011-03-01
Access Restriction	Subscribed
Subject Keyword	stent Stability and convergence of numerical methods projection methods for NavierStokes equations Physiological flows porous interface Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods blood flow Nitsche's method stabilized finite element Navier-Stokes equations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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