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

Abstract

This paper concerns 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 theoretical analysis is based on the weighted Necas inequality. 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. Numerical experiments show that the suggested preconditioner leads to an iterative method insensitive to the variation of mesh size and the regularization parameter of the fluid model.