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We extend our recent work on the creeping flow of a Bingham fluid in alid-driven cavity, to the study of inertial effects, using a finite volumemethod and the Papanastasiou regularisation of the Bingham constitutive model[J. Rheology 31 (1987) 385-404]. The finite volume method used belongs to avery popular class of methods for solving Newtonian flow problems, which usethe SIMPLE algorithm to solve the discretised set of equations, and havematured over the years. By regularising the Bingham constitutive equation it iseasy to extend such a solver to Bingham flows since all that this requires isto modify the viscosity function. This is a tempting approach, since itrequires minimum programming effort and makes available all the existingfeatures of the mature finite volume solver. On the other hand, regularisationintroduces a parameter which controls the error in addition to the gridspacing, and makes it difficult to locate the yield surfaces. Furthermore, theequations become stiffer and more difficult to solve, while the discontinuityat the yield surfaces causes large truncation errors. The present work attemptsto investigate the strengths and weaknesses of such a method by applying it tothe lid-driven cavity problem for a range of Bingham and Reynolds numbers (upto 100 and 5000 respectively). By employing techniques such as multigrid, localgrid refinement, and an extrapolation procedure to reduce the effect of theregularisation parameter on the calculation of the yield surfaces (Liu et al.J. Non-Newtonian Fluid Mech. 102 (2002) 179-191), satisfactory results areobtained, although the weaknesses of the method become more noticeable as theBingham number is increased.

Performance of the finite volume method in solving regularised Bingham flows: inertia effects in the lid-driven cavity flow