A NITSCHE-BASED CUT FINITE ELEMENT METHOD FOR A FLUID-STRUCTURE INTERACTION PROBLEM

作者：Massing Andre^*; Larson Mats G; Logg Anders; Rognes Marie E

来源：Communications in Applied Mathematics and Computational Science, 2015, 10(2): 97-120.

DOI：10.2140/camcos.2015.10.97

• fluid-structure interaction
• overlapping meshes
• cut finite element method
• embedded meshes
• stabilized finite element methods
• Nitsche's method

We present a new composite mesh finite element method for fluid-structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh that is embedded into a fixed background fluid mesh. The embedding allows for an arbitrary overlap of the fluid meshes. The coupling between the embedded and background fluid meshes is enforced using a stabilized Nitsche formulation that allows us to establish stability and optimal-order a priori error estimates. We consider here a steady state fluid-structure interaction problem where a hyperelastic structure interacts with a viscous fluid modeled by the Stokes equations. We evaluate an iterative solution procedure based on splitting and present three-dimensional numerical examples.

• 出版日期2015