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

Mikel Landajuela
INRIA, Paris
Thursday 10th December 2015
Aula Seminari
In this work we present a Nitsche-XFEM method for fluid-structure interaction problems involving a thin-walled elastic structure immersed in an incompressible fluid. The fluid domain is discretized with an unstructured mesh not fitted to the solid mid-surface mesh. The thin-walled nature of the immersed solid introduces jumps on the fluid stresses which, respectively, results in weak and strong discontinuities of the velocity and pressure fields across the interface. The approximation spaces allow to capture these discontinuous features through suitable enrichment of the intersected elements (see [1]). The kinematic/kinetic fluid-solid coupling is enforced consistently using a variant of Nitsche’s method involving cut elements. Robustness with respect to arbitrary interface/element intersections is guaranteed through a ghost penalty stabilization (see [2]). For the temporal discretization, several coupling schemes with different degrees of fluid-solid splitting (implicit, semi-implicit and explicit) are investigated. In particular, we address the extension of the explicit coupling paradigm introduced in [3] to the unfitted mesh framework. The stability and convergence properties of the methods proposed are rigorously analyzed in a representative linear setting. Several numerical examples, involving static and moving interfaces, illustrate the performance of the methods. [1] A. Hansbo and P. Hansbo. A finite element method for the simula- tion of strong and weak discontinuities in solid mechanics. Comput. Methods Appl. Mech. Engrg., 193(33-35):3523–3540, 2004. [2] E. Burman and P. Hansbo, Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes problem. M2AN Math. Model. Numer. Anal., 48(3):859–874, 2014. [3] M. Fernández, J. Mullaert, M. Vidrascu, Explicit Robin-Neumann schemes for the coupling of incompressible fluids with thin-walled structures, Comput. Methods Appl. Mech. Engrg. 267 (2013) 566–593. This seminar is organized within the PRIN 2012 Research project «Mathematical and numerical modeling of the cardiovascular system, and their clinical applications» Grant Registration number 201289A4LX_001, funded by MIUR – Project coordinator Prof. Luca Formaggia