Solution of Viscoplastic Flows With the Finite Volume/Multigrid Method

Abstract eng:
We investigate the performance of the finite volume method in solving viscoplastic flows. The square lid-driven cavity flow of a Bingham plastic is chosen as the test case and the constitutive equation is regularised as proposed by Papanastasiou [J. Rheol. 31 (1987) 385404]. The numerical results obtained for Bingham numbers up to 10 and Reynolds numbers up to 5000 compare favourably with reported results obtained through other methods. The effects of the Reynolds and Bingham numbers are also investigated. It is shown that the convergence rate of the standard SIMPLE pressure-correction algorithm, which is used to solve the algebraic equation system that is produced by the finite volume discretisation, severely deteriorates as the Bingham number increases, with a corresponding increase in the non-linearity of the equations. Using the SIMPLE algorithm in a multigrid context [Syrakos & Goulas, Int. J. Numer. Methods Fluids 52 (2006) 1215-1245] dramatically improves convergence, although the multigrid convergence rates are not as high as those for Newtonian flows.

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