## On the Performance of Certain Iterative Solvers for Coupled Systems Arising in Discretization of Non-Newtonian Flow Equations

• Iterative solution of large scale systems arising after discretization and linearization of the unsteady non-Newtonian Navier–Stokes equations is studied. cross WLF model is used to account for the non-Newtonian behavior of the fluid. Finite volume method is used to discretize the governing system of PDEs. Viscosity is treated explicitely (e.g., it is taken from the previous time step), while other terms are treated implicitly. Different preconditioners (block–diagonal, block–triangular, relaxed incomplete LU factorization, etc.) are used in conjunction with advanced iterative methods, namely, BiCGStab, CGS, GMRES. The action of the preconditioner in fact requires inverting different blocks. For this purpose, in addition to preconditioned BiCGStab, CGS, GMRES, we use also algebraic multigrid method (AMG). The performance of the iterative solvers is studied with respect to the number of unknowns, characteristic velocity in the basic flow, time step, deviation from Newtonian behavior, etc. Results from numerical experiments are presented and discussed.

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Verfasserangaben: O. Iliev, J. Linn, M. Moog, D. Niedziela, V. Starikovicius urn:nbn:de:hbz:386-kluedo-13428 Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (62) Bericht Englisch 2004 2004 Fraunhofer-Institut für Techno- und Wirtschaftsmathematik 26.07.2004 Non-Newtonian flow; Performance of iterative solvers; Preconditioners Fraunhofer (ITWM) 5 Naturwissenschaften und Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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