Solution of the square lid-driven cavity flow of a Bingham plastic using the finite volume method

Abstract

We investigate the performance of the finite volume method in solving viscoplastic flows. The creeping 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) 385-404]. 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. It is shown that using the SIMPLE algorithm in a multigrid context dramatically improves convergence, although the multigrid convergence rates are much worse than for Newtonian flows. The numerical results obtained for Bingham numbers as high as 1000 compare favourably with reported results of other methods.

References in corpus (2)

• Estimate of the truncation error of a finite volume discretisation of the Navier-Stokes equations on colocated grids
• Finite volume adaptive solutions using SIMPLE as smoother

Cited by in corpus (6)

• A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods
• Performance of the finite volume method in solving regularised Bingham flows: inertia effects in the lid-driven cavity flow
• An Accelerated Dual Proximal Gradient Method for Applications in Viscoplasticity
• Highly parallelisable simulations of time-dependent viscoplastic fluid flow simulations with structured adaptive mesh refinement
• Viscoplastic flow in an extrusion damper
• A semismooth Newton method for implicitly constituted non-Newtonian fluids and its application to the numerical approximation of Bingham flow