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

Journal of Non-Newtonian Fluid Mechanics

Volumn 208-209, Issue , 2014, Pages 88-107

  Syrakos, Alexandros ^a   Georgiou, Georgios C ^a   Alexandrou, Andreas N ^a  

^a UNIVERSITY OF CYPRUS   (Cyprus)

Author keywords

Adaptive mesh refinement; Bingham flow; Finite volume method; Lid driven cavity; Regularisation; SIMPLE

Indexed keywords

REYNOLDS NUMBER;

ADAPTIVE MESH REFINEMENT; BINGHAM FLOW; LID-DRIVEN CAVITIES; REGULARISATION; SIMPLE;

FINITE VOLUME METHOD;

EID: 84899964603     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2014.03.004     Document Type: Article

References (57)

1. Ferziger J.H., Peric M. Computational Methods for Fluid Dynamics 2002, Springer. 3rd ed.
2. Patankar S.V., Spalding D.B. A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int. J. Heat Mass Transfer 1972, 15:1787-1806.
3. Ferrás L.L., Nóbrega J.M., Pinho F.T. Implementation of slip boundary conditions in the finite volume method: new techniques. Int. J. Numer. Methods Fluids 2013, 72:724-747.
4. Sivaloganathan S., Shaw G.J. A multigrid method for recirculating flows. Int. J. Numer. Methods Fluids 1988, 8:17-440.
5. Hortmann M., Peric M., Scheuerer G. Finite volume multigrid prediction of laminar natural convection: benchmark solutions. Int. J. Numer. Methods Fluids 1990, 11:189-207.
6. Bercovier M., Engelman M. A finite-element method for incompressible non-Newtonian flows. J. Comput. Phys. 1980, 36:313-326.
7. Papanastasiou T.C. Flows of materials with yield. J. Rheol. 1987, 31:385-404.
8. O'Donovan E., Tanner R. Numerical study of the Bingham squeeze film problem. J. Non-Newtonian Fluid Mech. 1984, 15:75-83.
9. Frigaard I.A., Nouar C. On the usage of viscosity regularisation methods for visco-plastic fluid flow computation. J. Non-Newtonian Fluid Mech. 2005, 127:1-26.
10. Dean E.J., Glowinski R., Guidoboni G. On the numerical simulation of Bingham visco-plastic flow: old and new results. J. Non-Newtonian Fluid Mech. 2007, 142:36-62.
11. Naccache M.F., Barbosa R.S. Creeping flow of viscoplastic materials through a planar expansion followed by a contraction. Mech. Res. Commun. 2007, 34:423-431.
12. Mossaz S., Jay P., Magnin A. Criteria for the appearance of recirculating and non-stationary regimes behind a cylinder in a viscoplastic fluid. J. Non-Newtonian Fluid Mech. 2010, 165:1525-1535.
13. Turan O., Chakraborty N., Poole R.J. Laminar natural convection of Bingham fluids in a square enclosure with differentially heated side walls. J. Non-Newtonian Fluid Mech. 2010, 165:901-913.
14. Filali A., Khezzar L., Mitsoulis E. Some experiences with the numerical simulation of Newtonian and Bingham fluids in dip coating. Comput. Fluids 2013, 82:110-121.
15. Tokpavi D.L., Magnin A., Jay P. Very slow flow of Bingham viscoplastic fluid around a circular cylinder. J. Non-Newtonian Fluid Mech. 2008, 154:65-76.
16. Nirmalkar N., Chhabra R., Poole R. On creeping flow of a Bingham plastic fluid past a square cylinder. J. Non-Newtonian Fluid Mech. 2012, 171:17-30.
17. Zamankhan P., Helenbrook B.T., Takayama S., Grotberg J.B. Steady motion of Bingham liquid plugs in two-dimensional channels. J. Fluid Mech. 2012, 705:258-279.
18. Fortin M., Glowinski R. Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems 1983, North-Holland, Amsterdam.
19. Glowinski R. Numerical Methods for Nonlinear Variational Problems 1984, Springer, New York.
20. Glowinski R., Wachs A. On the numerical simulation of viscoplastic fluid flow. Numerical Methods for Non-Newtonian Fluids, of Handbook of Numerical Analysis 2011, Vol. 16:483-717. Elsevier.
21. Vinay G., Wachs A., Agassant J.-F. Numerical simulation of non-isothermal viscoplastic waxy crude oil flows. J. Non-Newtonian Fluid Mech. 2005, 128:144-162.
22. Barnes H.A. The yield stress - a review or - everything flows?. J. Non-Newtonian Fluid Mech. 1999, 81:133-178.
23. Balmforth N.J., Frigaard I.A., Ovarlez G. Yielding to stress: recent developments in viscoplastic fluid mechanics. Ann. Rev. Fluid Mech. 2014, 46:121-146.
24. Mendes P.S., Dutra E.S. Viscosity function for yield-stress liquids. Appl. Rheol. 2004, 14:296-302.
25. Dimakopoulos Y., Pavlidis M., Tsamopoulos J. Steady bubble rise in Herschel Bulkley fluids and comparison of predictions via the augmented Lagrangian method with those via the Papanastasiou model. J. Non-Newtonian Fluid Mech. 2013, 200:34-51.
26. Syrakos A., Georgiou G., Alexandrou A. Solution of the square lid-driven cavity flow of a Bingham plastic using the finite volume method. J. Non-Newtonian Fluid Mech. 2013, 195:19-31.
27. Roquet N., Saramito P. An adaptive finite element method for Bingham fluid flows around a cylinder. Comput. Methods Appl. Mech. Eng. 2003, 192:3317-3341.
28. Zhang J. An augmented Lagrangian approach to Bingham fluid flows in a lid-driven square cavity with piecewise linear equal-order finite elements. Comput. Methods Appl. Mech. Eng. 2010, 199:3051-3057.
29. Syrakos A., Goulas A. Finite volume adaptive solutions using SIMPLE as smoother. Int. J. Numer. Methods Fluids 2006, 52:1215-1245.
30. Syrakos A., Efthimiou G., Bartzis J.G., Goulas A. Numerical experiments on the efficiency of local grid refinement based on truncation error estimates. J. Comput. Phys. 2012, 231:6725-6753.
31. Shankar P.N., Deshpande M.D. Fluid mechanics in the driven cavity. Ann. Rev. Fluid Mech. 2000, 32:93-136.
32. Erturk E. Discussions on driven cavity flow. Int. J. Numer. Methods Fluids 2009, 60:275-294.
33. Ghia U., Ghia K.N., Shin C.T. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. J. Comput. Phys. 1982, 48:387-411.
34. Botella O., Peyret R. Benchmark spectral results on the lid-driven cavity flow. Comput. Fluids 1998, 27:421-433.
35. Pan F., Acrivos A. Steady flows in rectangular cavities. J. Fluid Mech. 1967, 28:643-655.
36. Koseff J.R., Street R.L. The lid-driven cavity flow: a synthesis of qualitative and quantitative observations. J. Fluids Eng. 1984, 106:390-398.
37. Rhee H.S., Koseff J.R., Street R.L. Flow visualization of a recirculating flow by rheoscopic liquid and liquid crystal techniques. Exp. Fluids 1984, 2:57-64.
38. Albensoeder S., Kuhlmann H.C., Rath H.J. Three-dimensional centrifugal-flow instabilities in the lid-driven-cavity problem. Phys. Fluids 2001, 13:121-135.
39. Albensoeder S., Kuhlmann H.C. Accurate three-dimensional lid-driven cavity flow. J. Comput. Phys. 2005, 206:536-558.
40. Mitsoulis E., Zisis T. Flow of Bingham plastics in a lid-driven square cavity. J. Non-Newtonian Fluid Mech. 2001, 101:173-180.
41. Sanchez F. Application of a first-order operator splitting method to Bingham fluid flow simulation. Comput. Math. Appl. 1998, 36:71-86.
42. Yu Z., Wachs A. A fictitious domain method for dynamic simulation of particle sedimentation in Bingham fluids. J. Non-Newtonian Fluid Mech. 2007, 145:78-91.
43. Muravleva E.A., Olshanskii M.A. Two finite-difference schemes for calculation of Bingham fluid flows in a cavity. Russian J. Numer. Anal. Math. Modell. 2008, 23:615-634.
44. Neofytou P. A 3rd order upwind finite volume method for generalised Newtonian fluid flows. Adv. Eng. Software 2005, 36:664-680.
45. Elias R., Martins M., Coutinho A. Parallel edge-based solution of viscoplastic flows with the SUPG/PSPG formulation. Comput. Mech. 2006, 38:365-381.
46. Frey S., Silveira F.S., Zinani F. Stabilized mixed approximations for inertial viscoplastic fluid flows. Mech. Res. Commun. 2010, 37:145-152.
47. Prashant, Derksen J.J. Direct simulations of spherical particle motion in Bingham liquids. Comput. Chem. Eng. 2011, 35:1200-1214.
48. dos Santos D.D., Frey S., Naccache M.F., de Souza Mendes P. Numerical approximations for flow of viscoplastic fluids in a lid-driven cavity. J. Non-Newtonian Fluid Mech. 2011, 166:667-679.
49. Vola D., Boscardin L., Latché J. Laminar unsteady flows of Bingham fluids: a numerical strategy and some benchmark results. J. Comput. Phys. 2003, 187:441-456.
50. Syrakos A., Goulas A. Estimate of the truncation error of finite volume discretization of the Navier-Stokes equations on collocated grids. Int. J. Numer. Methods Fluids 2006, 50:103-130.
51. Brandt A. Multi-level adaptive solutions to boundary-value problems. Math. Comput. 1977, 31:333-390.
52. Trottenberg U., Oosterlee C., Schuller A. Multigrid 2001, Academic Press.
53. Fraysse F., de Vicente J., Valero E. The estimation of truncation error by τ-estimation revisited. J. Comput. Phys. 2012, 231:3457-3482.
54. Burgos G.R., Alexandrou A.N., Entov V. On the determination of yield surfaces in Herschel-Bulkley fluids. J. Rheol. 1999, 43:463-483.
55. Liu B.T., Muller S.J., Denn M.M. Convergence of a regularization method for creeping flow of a Bingham material about a rigid sphere. J. Non-Newtonian Fluid Mech. 2002, 102:179-191.
56. Tsamopoulos J.A., Chen M.E., Borkar A.V. On the spin coating of viscoplastic fluids. Rheol. Acta 1996, 35:597-615.
57. Evans K.J., Knoll D.A., Pernice M. Development of a 2-D algorithm to simulate convection and phase transition efficiently. J. Comput. Phys. 2006, 219:404-417.