Glowinski / Xu Numerical Methods for Non-Newtonian Fluids

Special Volume
1. Auflage 2010
ISBN: 978-0-08-093202-6
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, Band Volume 16, 824 Seiten

Reihe: Handbook of Numerical Analysis

Non-Newtonian flows and their numerical simulations have generated an abundant literature, as well as many publications and references to which can be found in this volume's articles. This abundance of publications can be explained by the fact that non-Newtonian fluids occur in many real life situations: the food industry, oil & gas industry, chemical, civil and mechanical engineering, the bio-Sciences, to name just a few. Mathematical and numerical analysis of non-Newtonian fluid flow models provide challenging problems to partial differential equations specialists and applied computational mathematicians alike. This volume offers investigations. Results and conclusions that will no doubt be useful to engineers and computational and applied mathematicians who are focused on various aspects of non-Newtonian Fluid Mechanics. - New review of well-known computational methods for the simulation viscoelastic and viscoplastic types - Discusses new numerical methods that have proven to be more efficient and more accurate than traditional methods - Articles that discuss the numerical simulation of particulate flow for viscoelastic fluids

Autoren/Hrsg.

Glowinski, R.

Xu, Jinchao

Inhaltsverzeichnis

1;Front Cover;1
2;Handbook of Numerical Analysis;3
3;Copyright;5
4;General Preface;6
5;Table of Contents;8
6;Foreword;20
7;Numerical Methods for Grade-Two Fluid Models: Finite-Element Discretizations and Algorithms;24
7.1;Chapter 1. Theoretical Results;28
7.1.1;1.0. Foreword;28
7.1.2;1.1. Introduction and preliminaries;28
7.1.3;1.2. Constitutive and momentum equations;36
7.1.4;1.3. A brief survey of theoretical results;38
7.1.5;1.4. Splitting the two-dimensional problem;46
7.2;Chapter 2. Discretizing the Steady Split No-Slip Problem;54
7.2.1;2.1. General centered schemes;54
7.2.2;2.2. Centered schemes: Examples;69
7.2.3;2.3. Centered schemes: Successive approximations;82
7.2.4;2.4. Upwind schemes;89
7.3;Chapter 3. Discretizing the Time-Dependent No-Slip Problem;104
7.3.1;3.1. Introduction;104
7.3.2;3.2. Splitting the problem;107
7.3.3;3.3. Fully discrete centered schemes;126
7.3.4;3.4. Fully discrete upwind scheme with discontinuous Galerkin;137
7.4;Chapter 4. A Least-Squares Approach for the No-Slip Problem;148
7.4.1;4.1. Least-squares schemes for the steady no-slip problem;148
7.4.2;4.2. An approximate gradient algorithm;158
7.4.3;4.3. Application to the time-dependent problem;163
7.5;Chapter 5. The Steady Problem with Tangential Boundary Conditions;166
7.5.1;5.1. Some theoretical results;166
7.5.2;5.2. Centered schemes for the nonhomogeneous problem;172
7.5.3;5.3. Upwind schemes for the nonhomogeneous problem;185
7.6;Chapter 6. Numerical Experiments;196
7.6.1;6.1. The steady problem;196
7.6.2;6.2. The time-dependent case;213
7.7;References;224
7.8;List of Notation;230
8;The Langevin and Fokker–Planck Equations in Polymer Rheology;234
8.1;Chapter 1. Introduction;236
8.1.1;1.1. The Langevin and Fokker–Planck equations;237
8.1.2;1.2. Recent progress in the mathematical analysis and numerical simulation of flows of polymeric fluids;246
8.1.3;1.3. Article summary;250
8.2;Chapter 2. Stochastic Simulation Techniques;254
8.2.1;2.1. Introduction to stochastic differential equations;254
8.2.2;2.2. First-generation micro–macro techniques;258
8.2.3;2.3. Second-generation micro–macro techniques;264
8.2.4;2.4. Implicit micro–macro schemes;270
8.2.5;2.5. Stochastic methods for reptation models;272
8.3;Chapter 3. Fokker--Planck-Based Numerical Methods;276
8.3.1;3.1. Dilute solutions, locally homogeneous flows;276
8.3.2;3.2. Numerical methods for flows without the local homogeneity assumption;285
8.3.3;3.3. Numerical methods for concentrated solutions;291
8.3.4;3.4. Models with high-dimensional configuration spaces;292
8.4;Chapter 4. Numerical Results;306
8.4.1;4.1. Second-generation micro–macro techniques;307
8.4.2;4.2. Fokker–Planck-based numerical methods for locally homogeneous flows of dilute polymeric solutions;312
8.4.3;4.3. Fokker–Planck-based numerical methods for nonhomogeneous flows of dilute polymeric solutions: steady Poiseuille flow in a narrow channel;315
8.4.4;4.4. Fokker–Planck-based numerical methods for melts and concentrated polymeric solutions: Couette flow of a Doi–Edwards fluid;316
8.4.5;4.5. Fokker–Planck-based numerical methods for high-dimensional configuration spaces;317
8.5;Acknowledgments;320
8.6;Bibliography;322
9;Viscoelastic Flows with Complex Free Surfaces: Numerical Analysis and Simulation;328
9.1;Chapter 1. Modeling of Viscoelastic Flows with Complex Free Surfaces;330
9.1.1;1.1. Macroscopic models;333
9.1.2;1.2. Mesoscopic models;335
9.1.3;1.3. Initial and boundary conditions;340
9.1.4;1.4. Summary;342
9.2;Chapter 2. Numerical Analysis of Simplified Problems;344
9.2.1;2.1. Numerical models for viscoelastic flows: a chronological review;344
9.2.2;2.2. Time discretization: an operator splitting scheme;353
9.2.3;2.3. The three fields stokes problem;355
9.2.4;2.4. A simplified Oldroyd-B problem;361
9.2.5;2.5. A simplified Hookean dumbbells problem;364
9.3;Chapter 3. Numerical Simulation of Viscoelastic Flows with Complex Free Surfaces;370
9.3.1;3.1. Space discretization: structured cells and finite elements;370
9.3.2;3.2. Extension to mesoscopic models;378
9.3.3;3.3. Numerical results;378
9.4;Acknowledgment;385
9.5;Bibliography;386
10;Stable Finite Element Discretizations for Viscoelastic Flow Models;394
10.1;1. Introduction;395
10.2;2. Flow maps, generalized Lie derivatives, and Riccati equations;396
10.3;3. General macroscopic viscoelastic models;402
10.4;4. Basic mathematical and physical properties of the models;409
10.5;5. Existing numerical methods for viscoelastic fluid models;412
10.6;6. A family of Eulerian–Lagrangian finite element methods;417
10.7;7. Fast and robust solvers for Stokes-type systems;429
10.8;8. Stability analysis and existence of discrete solutions;433
10.9;9. Implementation details and numerical experiments;443
10.10;10. Concluding remarks;448
10.11;Acknowledgments;449
10.12;References;450
11;Positive Definiteness Preserving Approaches for Viscoelastic Flow of Oldroyd-B Fluids: Applications to a Lid-Driven Cavity Flow and a Particulate Flow;456
11.1;1. Introduction;456
11.2;2. Particulate flow;457
11.3;3. Cavity flow;484
11.4;Acknowledgments;501
11.5;Bibliography;502
12;On the Numerical Simulation of Viscoplastic Fluid Flow;506
12.1;Chapter 1. Viscoplastic Fluid Flow: A Review;510
12.1.1;1. Introduction;510
12.1.2;2. Applications;513
12.1.3;3. Constitutive laws;517
12.1.4;4. Numerical methods;521
12.1.5;5. A brief history of computational viscoplasticity;530
12.1.6;6. Conclusion;534
12.2;Chapter 2. Bingham Flow In Cylinders and Cavities;536
12.2.1;7. Introduction and Synopsis;536
12.2.2;8. On the modeling of Bingham viscoplastic flow;537
12.2.3;9. Bingham flow in cylinders: (I) Formulation;539
12.2.4;10. Bingham flow in cylinders: (II) the regularization approach;539
12.2.5;11. Bingham flow in cylinders: (III) variational inequality formulation. The multiplier approach;540
12.2.6;12. Bingham flow in cylinders: (IV) time-discretization of problem (11.1);546
12.2.7;13. Bingham flow in cylinders: (V) steady flow;551
12.2.8;14. Bingham flow in cylinders: (VI) an augmented Lagrangian approach to the solution of problem (13.7);563
12.2.9;15. Bingham flow in cylinders: (VII) finite-element approximation;566
12.2.10;16. Bingham flow in cylinders: (VIII) numerical experiments;568
12.2.11;17. Bingham flow in cavities;573
12.3;Chapter 3. Numerical Simulation of Nonisothermal, Compressible and Thixotropic Viscoplastic Flow: An Augmented Lagrangian Finite-Volume Approach;592
12.3.1;18. Generalities: synopsis;592
12.3.2;19. Governing equations;597
12.3.3;20. Augmented Lagrangian-based solution algorithms;600
12.3.4;21. A finite-volume scheme;610
12.3.5;22. Solution of the linear systems;624
12.3.6;23. Numerical experiments: wall-driven cavity creeping flow;627
12.3.7;24. Study of nonisothermal incompressible flow in pipelines;635
12.3.8;25. Transient isothermal compressible viscoplastic flow in a pipeline;650
12.3.9;26. Transient isothermal compressible and thixotropic flow in a pipeline: the isothermal restart of waxy crude oil flow;669
12.3.10;27. Additional comments on the augmented Lagrangian/finite-volume methodology: new challenges for waxy crude oil flow;680
12.4;Chapter 4. Application of Fictitious Domain Methods to the Numerical Simulation of Viscoplastic Flow;682
12.4.1;28. Introduction. Synopsis;682
12.4.2;29. Steady flow of a Bingham fluid through an eccentric annular cross-section;683
12.4.3;30. Dynamical simulation of particle sedimentation in a Bingham fluid;711
12.4.4;31. Further comments on distributed Lagrange multiplier/fictitious domain methods for Bingham fluid flow;731
12.5;Acknowledgments;733
12.6;References;734
13;Modeling, Simulation and Optimization of Electrorheological Fluids;742
13.1;1. Introduction;742
13.2;2. Mathematical models for electrorheological fluid flows;746
13.3;3. Numerical solution of electrorheological fluid flows;776
13.4;4. Numerical simulation and optimization of electrorheological devices;790
13.5;Acknowledgments;807
13.6;Bibliography;808
14;Index;818
15;Color plates;826