Uzawa-like methods for numerical modeling of unsteady viscoplastic Bingham medium flows

Applied Numerical Mathematics

Volumn 93, Issue , 2015, Pages 140-149

  Muravleva, Larisa ^a  

^a NONE

Author keywords

Bingham medium; Variational inequalities; Viscoplasticity

Indexed keywords

ALGORITHMS; VARIATIONAL TECHNIQUES; VISCOPLASTICITY;

BENCH-MARK PROBLEMS; BINGHAM; LID-DRIVEN SQUARE CAVITY; RHEOLOGICAL MODELING; STEADY-STATE PROBLEMS; TWO-DIMENSIONAL FLOW; VARIATIONAL INEQUALITIES; VISCOPLASTIC FLUID;

NUMERICAL METHODS;

EID: 84925290981     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2014.06.001     Document Type: Article

References (23)

1. G.A. Baker, V.A. Dougalis, and O.A. Karakashian On a higher order accurate fully discrete Galerkin approximation to the Navier-Stokes equations Math. Comput. 39 1982 339 375
2. E.J. Dean, R. Glowinski, and G. Guidoboni On the numerical simulation of Bingham visco-plastic flow: old and new results J. Non-Newton. Fluid Mech. 142 2007 36 62
3. J.C. De Los Reyes, and S. Gonzalez Andrade A combined BDF-semismooth Newton approach for time-dependent Bingham flow Numer. Methods Partial Differ. Equ. 28 2012 834 860
4. G. Duvaut, and J.L. Lions Inequalities in Mechanics and Physics 1976 Springer-Verlag Berlin
5. I. Ekeland, and R. Temam Convex Analysis and Variational Problems 1976 North-Holland Amsterdam
6. M. Fortin, and R. Glowinski Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems 1983 North-Holland Amsterdam
7. I.A. Frigaard, and C. Nouar On the usage of a viscosity regularisation methods for visco-plastic fluid flow computation J. Non-Newton. Fluid Mech. 127 2005 1 26
8. I.A. Frigaard, and D. Ryan Flow of a visco-plastic fluid in a channel of slowly varying width J. Non-Newton. Fluid Mech. 123 2004 67 83
9. R. Glowinski, J.L. Lions, and R. Tremolieres Numerical Analysis of Variational Inequalities 1981 North-Holland Amsterdam
10. R. Glowinski, and A. Wachs Numerical Methods for Non-Newtonian Fluids: Handbook of Numerical Analysis, vol. 16 2011 Elsevier 483 717
11. S.K. Godunov, and V.S. Ryabenkii The Difference Schemes: Introduction to the Theory 1977 Nauka Moscow (in Russian)
12. J.L. Guermond, P. Minev, and Jie Shen An overview of projection methods for incompressible flows Comput. Methods Appl. Mech. Eng. 195 2006 6011 6045
13. G.I. Marchuk Methods of Numerical Mathematics 2nd edition 1982 Springer-Verlag New York
14. E. Mitsoulis, and Th. Zisis Flow of Bingham plastics in a lid-driven cavity J. Non-Newton. Fluid Mech. 101 2001 173 180
15. L.V. Muravleva, and E.A. Muravleva Uzawa-like algorithm on semi-staggered grids for unsteady Bingham medium flows Russ. J. Numer. Anal. Math. Model. 24 6 2009 543 563
16. L.V. Muravleva, E.A. Muravleva, G.C. Georgiou, and E. Mitsoulis Numerical simulations of cessation flows of a Bingham plastic with the Augmented Lagrangian Method J. Non-Newton. Fluid Mech. 165 2010 544 550
17. P. Saramito, and N. Roquet An adaptive finite element method for viscoplastic fluid flows in pipes Comput. Methods Appl. Mech. Eng. 190 40 2001 5391 5412
18. R. Temam Navier-Stokes Equations: Theory and Numerical Analysis 1977 North-Holland Pub. Company
19. L.J.P. Timmermans, P.D. Minev, and F.N. Van De Vosse An approximate projection scheme for incompressible flow using spectral elements Int. J. Numer. Methods Fluids 22 1996 673 688
20. J. Van Kan A second-order accurate pressure-correction scheme for viscous incompressible flow SIAM J. Sci. Stat. Comput. 7 3 1986 870 891
21. G. Vinay, A. Wachs, and J.-F. Agassant Numerical simulation of non-isothermal viscoplastic waxy crude oil flows J. Non-Newton. Fluid Mech. 128 2005 144 162
22. D. Vola, L. Boscardin, and J.C. Latche Laminar unsteady flows of Bingham fluids: a numerical strategy and some benchmark results J. Comp. Physiol. 187 2003 441 456
23. Z. Yu, and A. Wachs A fictitious domain method for dynamic simulation of particle sedimentation in Bingham fluids J. Non-Newton. Fluid Mech. 145 2007 78 91