Finite-difference schemes for the computation of viscoplastic medium flows in a channel

Mathematical Models and Computer Simulations

Volumn 1, Issue 6, 2009, Pages 768-779

  Muravleva, E A ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

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EID: 77950626531     PISSN: 20700482     EISSN: 20700490     Source Type: Journal    
DOI: 10.1134/S2070048209060118     Document Type: Article

References (21)

1. F. N. Shwedov, “La rigidite de liquids,” in Rapport Congr. Intern. Phys. (Paris, 1900), vol. 1, pp. 478–486.
2. F. C. Bingham, Fluidity and Plasticity (New York, 1922).
3. G. Genki, “Three-Dimensional Problem of Elastic and Plastic Equilibriums,” Izv. AN USSR, OTN, No. 2 (1937).
4. A. A. Il’yushin, “Deformation of Viscous-Plastic Body,” Uch. zapiski MGU, Mekhanika, vol. 39, (1940).
5. J. G. Oldroyd, “Two-Dimensional Plastic Flow of a Bingham Solid. A Plastic Boundary-Layer Theory for Slow Motion,” in Proc. Camb. Phil. Soc. (1947), vol. 43, pp. 383–395.
6. W. Prager, “On Slow Visco-Plastic Flow,” in Chapter in Studies in Mathematics and Mechanics, Volume Presented to Richard for Mises (Academic Press, 1954).
7. P. P. Mosolov and V. P. Myasnikov, “Variational methods in the theory of the fluidity of a viscous-plastic medium,” PMM, J. Mech. Appl. Math., 29, 545–577 (1965).
8. P. P. Mosolov and V. P. Myasnikov, “On stagnant flow regions of a viscous-plastic medium in pipes,” PMM, J. Mech. Appl. Math., 30, 841–854 (1966).
9. P. P. Mosolov and V. P. Myasnikov, “On qualitative singularities of the flow of a viscoplastic medium in pipes,” PMM, J. Mech. Appl. Math., 31, 609–613 (1967).
10. G. Duvaut and J. L. Lions, Inequalities in Mechanics and Physics (Springer-Verlag, 1976; Nauka, Moscow, 1980).
11. P. P. Mosolov and V. P. Myasnikov, Variational Methods in the Theory of Rigid-Viscous-Plastic Mediums Flows (Izd-vo MGU, Moscow, 1971) [in Russian].
12. E. J. Dean, R. Glowinski, and G. Guidoboni, “On the Numerical Simulation of Bingham Visco-Plastic Flow: Old and New Results,” J. Non-Newtonian Fluid Mech. 142, 36–62 (2007).
13. R. Glowinski, J. L. Lions, and R. Tremolieres, Analyse Numerique des Inequations. Variationnelles (Dunod, Paris, 1976; Mir, Moscow, 1979).
14. R. Glowinski, Numerical Methods for Nonlinear Variational Problems (Springer-Verlag, New York, 1984).
15. M. M. Karchevskii and A. D. Lyashko, Difference Schemes for Nonlinear Problems of Mathematical Physics (izd-vo KGU, Kazan, 1976) [in Russian].
16. A. V. Lapin, Introduction into Variational Inequalities Theory (Izd-vo KGU, Kazan, 1981) [in Russian].
17. A. V. Lapin, Grid Approximations of Variational Inequalities (Izd-vo KGU, Kazan, 1984) [in Russian].
18. N. Roquet and P. Saramito, “An Adaptive Finite Element Method for Viscoplastic Fluid Flows in Pipes,” Compur. Meth. Appl. Mech. Eng. 190(40), 5391–5412 (2001).
19. M. A. Moyers-Gonzalez and I. A. Frigaard, “Numerical Solution of Duct Flows of Multiple Visco-Plastic Fluids,” Non-Newtonian Fluid Mech. 122, 227–241 (2004).
20. R. R. Huilgol and Z. You, “Application of the Augmented Lagrangian Method to Steady Pipe Flows of Bingham, Casson and Herschel-Bulkley Fluids,” J. Non-Newtonian Fluid Mech. 128, 126–143 (2005).
21. C. Fletcher, Computation Methods in Liquid Dynamics (Springer-Verlag, Heidelberg, 1991; Mir, Moscow, 1991), vol. 2.