Direct simulation of rigid particles in a viscoelastic fluid

In this paper, we present a numerical method which performs the direct simulation of 2D viscoelastic suspensions. Objectives. Interactions between viscoelastic fluids of Oldroyd type, including inertial effects, and a large number of rigid disks or ellipsoids are addressed. Method. The numerical method is built upon a fictitious domain approach which consists in defining the fluid-structure problem over the whole domain (fluid+solid), see e.g. [1]. In the Newtonian case [2, 3], the resulting variational formulation, although classical, uses non-standard functional spaces which include the rigidity constraints. From the numerical point of view, these constraints can be addressed by penalty methods, leading to the possible use of standard finite elements solvers with fixed structured meshes. We show how this approach can be adapted to viscoelastic fluids of Oldroyd type. Results. Two types of configurations are investigated in dilute and dense regimes: sedimentation of circular particles and shear flows with ellipsoidal particles.