Numerical Simulation of the Motion of Rigid Particles in Generalized Newtonian Fluids using a Hyper-Viscosity Method

Abstract

We present a new numerical method to handle fluid-rigid body interaction problems. The analysis is carried out for incompressible generalized Newtonian fluids, but more general constitutive equations can be considered with little changes in the method. The work is motivated by the investigation of interaction problems occurring in the human cardiovascular system. In this framework the rigid bodies may be blood particles, clots, valves or any structure that we may assume to move rigidly in blood. This method is based in a variational formulation of the fully coupled problem in the whole fluid/solid domain, in which constraints are introduced to enforce the rigid motion of the body and the equilibria of forces and stresses at the interface. The main feature of the method consists in introducing a penalty parameter that relaxes the constraints and allows for the solution of an associated unconstrained problem. The convergence of the solution of the relaxed problem is established and some numerical simulations are performed using common benchmarks for this type of problems.