A fictitious domain approach for the Stokes problem based on the extended finite element method
This work addresses the challenge of simulating fluid flow in domains with complex or moving boundaries for computational fluid dynamics researchers.
The authors extend a fictitious domain method based on the eXtended Finite Element Method to the Stokes problem, enabling computations on non-matching grids. Numerical tests demonstrate the method's capabilities, but no concrete performance numbers are provided.
In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries do not match. A mixed finite element method is used for fluid flow. The interface between the fluid and the structure is localized by a level-set function. Dirichlet boundary conditions are taken into account using Lagrange multiplier. A stabilization term is introduced to improve the approximation of the normal trace of the Cauchy stress tensor at the interface and avoid the inf-sup condition between the spaces for velocity and the Lagrange multiplier. Convergence analysis is given and several numerical tests are performed to illustrate the capabilities of the method.