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This study proposes to develop and investigate different iterative solvers for non‐Newtonian flow equations.

Existing approaches for the time discretization of the flow equation and for an iterative solution of the discrete systems are discussed. Ideas for further development of existing preconditioners are proposed, implemented and investigated numerically.

A two‐level preconditioning, consisting of a transformation of the original system in the first step and subsequent preconditioning of the transformed system is suggested. The GMRES iterative method, which usually performs well when applied to academic problems, showed dissatisfactory performance for the type of industrial flow simulations investigated in this work. It was found that the BiCGStab method performed best in the tests presented here.

The iterative solvers considered here were investigated only for a certain class of polymer flows. More detailed studies for other non‐Newtonian flows should be carried out.

The work presented in this paper fills a gap related to the usage of efficient iterative methods for non‐Newtonian flow simulations.