Stabilized Methods for Generalized Newtonian Fluids Flows

In this paper we present Petrov-Galerkin finite element methods to solve the generalized Navier-Stokes-like equations which models nonNewtonian fluids flows. In the context of the generalized Stokes flow, to overcome the numerical difficulties arising from the power-law model and the incompressibility constraint, working with an apparent fluidity instead of the viscosity, it was presented in [1] a stabilized mixed finite element formulation in four variables. Without loosing the good properties of the formulation proposed in [1], in the present work we analyse the problem of non-Newtonian fluids flows in the presence of the convective term, resulting in a method with two iteration levels. The first one deals with the non linearity that comes from the constitutive equation. The other is in charge of solving the non linearity of the convection dominated feature of these problems, for which the CAU method, [2], can be used to approximate high gradient solutions related to boundary layer phenomena.