ϕ-FEM: an optimally convergent and easily implementable immersed boundary method for particulate flows and Stokes equations

We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called ϕ -FEM, that uses the description of the solid with a level-set function. One of the advantages of our method is the use of standard finite element spaces and classical integration tools, while maintaining the optimal convergence (theoretically in the H 1 norm for the velocity and L 2 for pressure; numerically also in the L 2 norm for the velocity).