Numerical simulation of two-dimensional Bingham fluid flow by semismooth Newton methods

Journal of Computational and Applied Mathematics

Volumn 235, Issue 1, 2010, Pages 11-32

  De Los Reyes, Juan Carlos ^a   González Andrade, Sergio ^a  

^a Research Group on Optimization   (Ecuador)

Author keywords

Bingham fluids; Elliptic variational inequalities; Semismooth Newton methods; Tikhonov regularization

Indexed keywords

BINGHAM FLUID; DIRICHLET; NEWTON ITERATIONS; NUMERICAL EXPERIMENTS; NUMERICAL SIMULATION; OPTIMALITY SYSTEM; SEMISMOOTH; SEMISMOOTH NEWTON ALGORITHM; SEMISMOOTH NEWTON METHOD; STRESS-FREE BOUNDARY CONDITIONS; SUPERLINEAR CONVERGENCE; TIKHONOV REGULARIZATION; VARIATIONAL INEQUALITIES;

CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; FLOW SIMULATION; FLUIDS; LINEAR EQUATIONS; TWO DIMENSIONAL; VARIATIONAL TECHNIQUES;

NEWTON-RAPHSON METHOD;

EID: 77955423305     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2010.02.026     Document Type: Article

References (44)

1. G. Duvaut, and J.-L. Lions Inequalities in Mechanics and Physics 1976 Springer-Verlag Berlin Translated from the French by C. W. John, Grundlehren der Mathematischen Wissenschaften, vol. 219
2. M. Fuchs, J.F. Grotowski, and J. Reuling On variational model for quasi-static Bingham fluids Mathematical Methods in the Applied Sciences 19 1996 991 1015
3. M. Fuchs, and G. Seregin Some remarks on non-Newtonian fluids including nonconvex perturbations of the Bingham and PowellEyring model for viscoplastic fluids Mathematical Models and Methods in Applied Sciences 7 3 1997 405 433
4. M. Fuchs, and G. Seregin Regularity results for the quasi-static Bingham variational inequality in dimensions two and three Mathematische Zeitschrift 227 1998 525 541 (Pubitemid 128382658)
5. M. Fuchs, and G. Seregin Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids Lecture Notes in Mathematics 2000 Springer-Verlag
6. R. Glowinski, J.-L. Lions, and R. Trmolires Numerical Analysis of Variational Inequalities Studies in Mathematics and its Applications vol. 8 1981 North-Holland Publishing Co. Amsterdam Translated from the French
7. R. Glowinski Numerical Methods for Nonlinear Variational Problems Springer Series in Computational Physics 1984 Springer-Verlag New York
8. E.J. Dean, R. Glowinski, and G. Guidoboni On the numerical simulation of Bingham visco-plastic flow: old and new results Journal of Non-Newtonian Fluid Mechanics 142 1-3 2007 36 62
9. J.C. De Los Reyes, and S. Gonzlez Path following methods for steady laminar Bingham flow in cylindrical pipes M2AN. Mathematical Modelling and Numerical Analysis 43 1 2009 81 117
10. T.C. Papanastasiou Flow of materials with yields Journal of Rheology 31 1987 385 404
11. N. Roquet, Simulation numrique d'coulements de fluides viscoplastiques par un algorithme de Lagrangien augment et une mthode d'lments finis incompressibles, DEA thse, Universit d'Orsay, Paris, Septembre 1996.
12. Piotr P. Grinevich, and Maxim A. Olshanskii An iterative method for the Stokes-type problem with variable viscosity SIAM Journal on Scientific Computing 31 5 2009 3959 3978
13. R. Glowinski Finite element methods for incompressible viscous flow P.G. Ciarlet, J.L. Lions, Numerical Methods for Fluids (Part 3) Handbook of Numerical Analysis vol. 9 2003 Elsevier
14. F.J. Snchez Application of a first-order operator splitting method to Bingham fluid flow simulation Computers & Mathematics with Applications 36 3 1998 71 86
15. P. Saramito, Simulation numrique d'coulements de fluides viscoplastiques par lments finis incompressibles et un mthode de directions alternes- applications, Doctorat in mcanique, L'institut National Polytechnique de Grenoble, Grenoble, Marz, 1990.
16. S.C. Brenner, and L.R. Scott The Mathematical Theory of Finite Element Methods second ed. Texts in Applied Mathematics vol. 15 2002 Springer-Verlag New York
17. M. Gunzburger NavierStokes equations for incompressible flows: finite-element methods R. Peyret, Handbook of Computational Fluid Mechanics 2004 Acad. Press 99 157
18. N. Roquet, and P. Saramito An adaptive finite element method for Bingham fluid flows around cylinder Computer Methods in Applied Mechanics and Engineering 192 2003 3317 3341
19. R. Dautray, and J.-L. Lions Mathematical Analysis and Numerical Methods for Science and Technology, vol. 2 2000 Springer-Verlag Berlin
20. J.L. Lions Optimal Control of Systems Governed by Partial Differential Equations 1971 Springer-Verlag
21. I. Ekeland, and R. Temam Convex Analysis and Variational Problems 1976 North-Holland Publishing Company Netherlands
22. B. Dacorogna Direct Methods in the Calculus of Variations Applied Mathematical Sciences vol. 78 1989 Springer-Verlag
23. J. Jahn Introduction to the Theory of Nonlinear Optimization 2007 Springer-Verlag
24. M. Hintermller, K. Ito, and K. Kunisch The primaldual active set strategy as a semi-smooth Newton method SIAM Journal on Optimization 13 3 2003 865 888
25. M. Hintermller, and K. Kunisch Path-following methods for a class of constrained minimization problems in function spaces SIAM Journal on Optimization 17 1 2006 159 187
26. M. Hintermller, and G. Stadler An infeasible primaldual algorithm for tv-based inf-convolution-type image restoration SIAM Journal on Scientific Computing 28 1 2006 1 23
27. K. Ito, and K. Kunisch Augmented Lagrangian methods for nonsmooth, convex optimization in Hilbert spaces Nonlinear Analysis 41 2000 591 616
28. K. Ito, and K. Kunisch Semi-smooth Newton methods for variational inequalities of the first kind M2AN. Mathematical Modelling and Numerical Analysis 37 1 2003 41 62
29. T.J. Abatzoglou Norm derivatives on spaces of operators Mathematische Annalen 239 2 1979 129 135
30. S. Gonzlez Andrade, Semismooth Newton and path-following methods for the numerical simulation of Bingham fluids, Ph.D. Thesis, Escuela Politcnica Nacional, QuitoEcuador, August 2008.
31. V. Girault, and P.-A. Raviart Finite Element Approximation of the NavierStokes Equations Lecture Notes in Mathematics vol. 749 1981 Springer
32. R. Temam NavierStokes Equations. Theory and Numerical Analysis 2001 AMS Chelsea Publishing USA
33. A. Quarteroni, and A. Valli Numerical Approximation of Partial Differential Equations Springer Series in Computational Mathematics vol. 23 1998 Springer-Verlag
34. J. Alberty, C. Carstensen, and S.A. Funken Remarks around 50 lines of Matlab: short finite element implementation Numerical Algorithms 20 2-3 1999 117 137
35. K. Atkinson, and W. Han Theoretical Numerical Analysis second ed. Texts in Applied Mathematics vol. 39 2005 Springer New York
36. J. Alberty, C. Carstensen, S.A. Funken, and R. Klose Matlab implementation of the finite element method in elasticity Computing 69 3 2002 239 263
37. P. Bochev, and M. Gunzburger An absolutely stable pressure-Poisson stabilized finite element method for the Stokes equations SIAM Journal on Numerical Analysis 42 3 2004 1189 1207
38. G. Stadler Semismooth Newton and augmented Lagrangian methods for a simplified friction problem SIAM Journal on Optimization 15 1 2004 39 62
39. C.R. Johnson Positive definite matrices The American Mathematical Monthly 77 3 1970 259 264
40. R. Mathias Matrices with positive definite Hermitian part: inequalities and linear systems SIAM Journal on Matrix Analysis and Applications 13 2 1992 640 654
41. L. Qin Convergence analysis of some algorithms for solving nonsmooth equations Mathematics of Operations Research 18 1 1993 227 244
42. D. Sun, and J. Han Newton and quasi-Newton methods for a class of nonsmooth equations and related problems SIAM Journal on Optimization 7 2 1997 463 480
43. S. Turek Efficient Solvers for Incompressible Flow Problems 1999 Springer Verlag Berlin
44. G.T. Gilbert Positive definite matrices and Sylvester's criterion The American Mathematical Monthly 98 1 1991 44 46