Numerical simulation of two-dimensional Bingham fluid flow by semismooth Newton methods
Journal of Computational and Applied Mathematics
Acquired Clustering Properties and Solution of Certain Saddle Point Systems
SIAM Journal on Matrix Analysis and Applications
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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 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.