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Article overview
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Performance of the finite volume method in solving regularised Bingham flows: inertia effects in the lid-driven cavity flow | | Alexandros Syrakos
; Georgios C. Georgiou
; Andreas N. Alexandrou
; | | Date: |
2 May 2016 | | Abstract: | We extend our recent work on the creeping flow of a Bingham fluid in a
lid-driven cavity, to the study of inertial effects, using a finite volume
method and the Papanastasiou regularisation of the Bingham constitutive model
[J. Rheology 31 (1987) 385-404]. The finite volume method used belongs to a
very popular class of methods for solving Newtonian flow problems, which use
the SIMPLE algorithm to solve the discretised set of equations, and have
matured over the years. By regularising the Bingham constitutive equation it is
easy to extend such a solver to Bingham flows since all that this requires is
to modify the viscosity function. This is a tempting approach, since it
requires minimum programming effort and makes available all the existing
features of the mature finite volume solver. On the other hand, regularisation
introduces a parameter which controls the error in addition to the grid
spacing, and makes it difficult to locate the yield surfaces. Furthermore, the
equations become stiffer and more difficult to solve, while the discontinuity
at the yield surfaces causes large truncation errors. The present work attempts
to investigate the strengths and weaknesses of such a method by applying it to
the lid-driven cavity problem for a range of Bingham and Reynolds numbers (up
to 100 and 5000 respectively). By employing techniques such as multigrid, local
grid refinement, and an extrapolation procedure to reduce the effect of the
regularisation parameter on the calculation of the yield surfaces (Liu et al.
J. Non-Newtonian Fluid Mech. 102 (2002) 179-191), satisfactory results are
obtained, although the weaknesses of the method become more noticeable as the
Bingham number is increased. | | Source: | arXiv, 1605.0590 | | Services: | Forum | Review | PDF | Favorites | |
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