Nitsche-XFEM for the coupling of an incompressible fluid with immersed thin-walled structures

Frédéric Alauzet 1 Benoit Fabrèges 2 Miguel Angel Fernández 2, * Mikel Landajuela 2
* Corresponding author
1 Gamma3 - Automatic mesh generation and advanced methods
ICD - Institut Charles Delaunay, Inria Saclay - Ile de France
2 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, UPMC - Université Pierre et Marie Curie - Paris 6, Inria de Paris
Abstract : In this paper we introduce a Nitsche-XFEM method for fluid-structure interaction problems involving a thin-walled elastic structure (Lagrangian formalism) immersed in an incompressible viscous fluid (Eulerian formalism). The fluid domain is discretized with an unstructured mesh not fitted to the solid mid-surface mesh. Weak and strong discontinuities across the interface are allowed for the velocity and pressure, respectively. The fluid-solid coupling is enforced consistently using a variant of Nitsche's method with cut-elements. Robustness with respect to arbitrary interface intersections is guaranteed through suitable stabilization. Several coupling schemes with different degrees of fluid-solid time splitting (implicit, semi-implicit and explicit) are investigated. A series of numerical tests in 2D, involving static and moving interfaces, illustrates the performance of the different methods proposed.
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Frédéric Alauzet, Benoit Fabrèges, Miguel Angel Fernández, Mikel Landajuela. Nitsche-XFEM for the coupling of an incompressible fluid with immersed thin-walled structures. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2016, 301, pp.300-335. ⟨10.1016/j.cma.2015.12.015⟩. ⟨hal-01149225v3⟩

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