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

Piotr P. Grinevich, Maxim A. Olshanskii
2009 SIAM Journal on Scientific Computing  
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 Nečas 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
more » ... ions 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. . Linear solver. In this section we deal with a discrete counterpart of (1.7). Here and in the remainder of the paper, the L 2 scalar product and associated norm are denoted by (·, ·) and · , respectively. Moreover, we will simply use the notation ν for the variable viscosity coefficient. To define the pressure space uniquely,
doi:10.1137/08744803 fatcat:6zdiublacfcmbhsjymx3oly65y