In contrast to most fluids, flowing powders do not exhibit viscosity
such that a
Newtonian rheology cannot accurately describe granular flow. Assuming that the
material is incompressible, dry, cohesionless, and perfectly rigid-plastic, generalized Navier-Stokes equations (`Schaeffer Model`)
have been derived where the velocity gradient has been replaced by the shear rate,
and the viscosity depends on pressure and shear rate which leads to mathematically
complex problems. In this report we present numerical algorithms to approximate these
highly nonlinear equations based on finite element methods. First of all, a Newton linearization
technique is applied directly to the continuous variational formulation.
The approximation of the incompressible velocity field is treated by using stabilized
nonconforming Stokes elements and we use a Pressure Schur Complement smoother as
defect correction inside of a direct multigrid approach to solve the linear
saddle-point problems with high numerical efficiency. The results of
computational experiments for two prototypical flow configurations are provided.