On preconditioning incompressible non-Newtonian flow problems

On preconditioning incompressible non-Newtonian flow problems

He, X.
Neytcheva, M.
Vuik, C.

Electrical Engineering, Mathematics and Computer Science

2013-07-31

This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space discretization we use the finite element method and utilize the two-by-two block structure of the matrices in the arising algebraic systems of equations. The Krylov subspace iterative methods are chosen to solve the linearized discrete systems and the development of computationally and numerically efficient preconditioners for the two-by-two block matrices is the main concern in this paper. In non-Newtonian flows, the viscosity is not constant and its variation is an important factor that effects the performance of some already known preconditioning techniques. In this paper we examine the performance of several preconditioners for variable viscosity applications, and improve them further to be robust with respect to variations in viscosity.

non-Newtonian flows
Navier-Stokes equations
two-by-two block systems
Krylov subspace methods
preconditioners

http://resolver.tudelft.nl/uuid:42c2dc6e-7509-45ba-b54e-85b6aec8964e

Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics

1389-6520

Reports of the Delft Institute of Applied Mathematics, 13-7

Institutional Repository

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(c)2013 He, X., Neytcheva, M., Vuik, C.