On numerical modelling of some non-newtonian fluids

In this contribution we will discuss different numerical techniques for the simulation of several non-newtonian flows. We will particularly concentrate on the multipolar barotropic flows, power-law flows as well as some Oldroyd type fluids used for the modelling in hemodynamics. In fact, numerical methods used here are the finite element methods and the combined finite volume-finite element methods. Special attention has to be payed to the stability of the discrete formulation. We present also some theoretical results for the uniqueness and existence of the solution of bipolar barotropic flow. Results of numerical experiments will be shown on video.