The Bingham fluid flow is a Stokes-type flow with shear-dependent
viscosity. If
and
, its equations read
and
where the velocity
In this talk we will address the discretization and linearization of these (nonlinear) equations. We will then propose a multilevel preconditioner with additive Schwartz smoothings for efficiently solving the resulting linear systems. Numerical experiments will be presented to demonstrate the effectiveness of both the nonlinear and linear solver.
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.