Monolithic stabilized finite element method for rigid body motions in the incompressible Navier-Stokes flow

Abstract : We propose a new immersed volume method for solving rigid body motions in the incompressible Navier-Stokes flow. The used monolithic formulation gives rise to an extra stress tensor in the Navier-Stokes equations coming from the presence of the structure in the fluid. The system is solved using a finite element variational multiscale (VMS) method, which consists in here of a decomposition for both the velocity and the pressure fields into coarse/resolved scales and fine/unresolved scales. The distinctive feature of the proposed approach resides in the efficient enrichment of the extra constraint. We assess the behaviour and accuracy of the proposed formulation in the simulation of 2D and 3D examples.