An Iterative Method for the Stokes-Type Problem with Variable Viscosity

The paper concerns with an iterative technique for solving discretized Stokes type equations with varying viscosity coefficient. We build a special block preconditioner for the discrete system of equations and perform an analysis revealing its properties. The subject of this paper is motivated by numerical solution of incompressible non-Newtonian fluid equations. In particular, the general analysis is applied to the linearized equations of the regularized Bingham model of viscoplastic fluid. Both theoretical analysis and numerical experiments show that the suggested preconditioner leads to a significant improvement of an iterative method convergence compared to a ‘standard’ preconditioner.