A fictitious domain/finite element method for particulate flows

The paper presents a finite element method for the direct numerical simulation of 3D incompressible fluid flows with suspended rigid particles. It uses the fictitious domain approach extending the fluid domain into the domain occupied by the particles. Although the idea for the present formulation came from the fictitious domain formulation of Glowinski et al. [J. Comput. Phys. 169 (2001) 363] it finally yielded a new scheme which allows for a more efficient integration of the system of equations and which is easier to implement algorithmically. It also avoids the need to grid the rigid particles and solves the entire problem on a single Eulerian grid. The spatial discretization is performed with P2−P1 finite elements but any other stable pair of approximations can be used. The present scheme is compared to a second order scheme based on the approach in Glowinski et al. [loc. cit.] using the test case of a single sphere in a viscous liquid. Its accuracy/costs performance is excellent.