Modeling of metal forming processes: implementation of an iterative solver in the flow formulation

Rigid-viscoplastic models of metal forming processes are mathematically formulated as non-linear Stokes problems: incompressible flows with variable viscosity, function of the point velocities. When discretizing those mathematical models using either u-p or velocity interpolated finite element formulations with the incompressibility imposed via penalty techniques, bad conditioned matrices are obtained. In this paper we discuss the implementation of an iterative solver for the efficient solution of the resulting equation systems.