A hyper-viscosity numerical method for the interaction of a shear-dependent fluid with a rigid body

Abstract

We present a numerical method for the simulation of the motion of rigid bodies in incompressible generalized Newtonian fluids. This work is motivated by the study of some physiological phenomena occurring in the human cardiovascular system where the bodies may be blood particles, clots or valves that we assume to be rigid. This new method is based on a variational formulation on the whole fluid/solid domain introducing constraints that enforce the rigid motion of the bodies. The core of this method consists in relaxing the constraints by introducing a penalty parameter (hyper-viscosity). The convergence to the solution of the relaxed problem is established. Finally we present some numerical results using a common benchmark for this type of problems.