Table of contents for Process modelling and simulation with finite element methods / William B.J. Zimmerman.


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Introduction to FEMLAB
W. B. Z. Zimmenran
0.1 Overview of the Book                                      1
0.2 An Example from the Model Library                        11
0.2 1 k-e Model of a Turbulent Static Mixer             12
0.2 2 Why the Tour of -e Model of a Turbulent Static
Mixer?                                            14
0.3 Chapter Synopsis                                         16
References                                                   22
FEMLAB and the Basics of Numerical Analysis                  23
W. B. J. Zimmerman
1.1 Introduction                                            23
12 Method 1: Root Finding                                   24
1 2.1 Root Finding: A Simple Application of the FEMLAB
Nonlinear Solver                                  25
1.2.2 Root Finding: Application to Flash Distillation   29
1.3 Method 2: Numerical Integration by Marching             33
1.3.1 Numerical Integration: A Simple Example           35
1.3.2 Numerical Integration: Tubular Reactor Design     38
1.4 Method 3: Numerical Integration of Ordinary Differential
Equations                                               44
1.5 Method 4: Linear Systems Analysis                       49
1.5.1 Heat Transfer in a Nonuniform Medium              55
1.6 Summary                                                 59
References                                                   59
Partial Differential Equations and the Finite Element Method    63
W. B. J Zimmerman and B. N. Hewakandamby
2.1 Introduction                                             63
2.1.1 Poisson's Equation: An Elliptic PDE               66
2.1 2 The Diffusion Equation: A Parabolic PDE           70
2. 1.3 The Wave Equation: A Hyperbolic PDE              75
2.1.4 Boundary Conditions                                85
2.1.5 Basic Elements                                     89
2.2 Summary                                                  105
References                                                   105
3   Mutiphysics                                                  107
W. B   Zimmerman
3.1 introduction                                             107
3.2  Buoyant Convection.                                     108
3.3 Unsteady Response of a Nonlinear Tubular Reactor         123
3.4 Heterogeneous Reaction in a Porous Catalyst Pellet       129
3.5 Discussion                                               135
References                                                   136
4   Extended Multiphysics                                        137
kW B. I Zimmerman, P  . Mcuhedov-Petrossyan and
G. A. Khomenko
4.1 Introduction                                             137
4.2 Heterogeneous Reaction in a Fixed Bed with Premixed Feed  140
4.3 Primacy of the Buffer Tank                               152
4 4 Linking the 2-D Buffer Tank to the 1-D Heterogeneous Reactor  162
4.5 Bioreactor Kinetics                                      167
4 6 Discussion                                               170
References                                                   171
5   Simulation and Nonlinear Dynamics                            173
V. B. J Zimmerman
5.1 Introduction                                             173
5.2 Rayleigh-Benard Convection                               178
5.2.1 Heating from Above                                 180
5.2.2 Heating from Below                                 184
5.2.3 Agreement with Thin Layer Theory                  190
5.3 Viscous Fingering Instabilities                          192
5.3.1 Streamfunction-Vorticity Model with Periodic BCs  202
5.4  Summary                                                 210
References                                                   212
6   Geometrc Continuation                                        215
W. B J. Zimmerman and A. F Routh
6.1 Introduction                                             215
6.2 Stationary Geometric Continuation: Pressure Drop in a
Channel with an Orifice Plate                            217
6.3 Transient Geometric Continuation: Film Drying          227
6 4 Summary                                                241
6.5 End Note: Solver Parameters for Problems with Pointwise
Weak Terms                                            242
References                                                 243
7   Coupling X ariables Revisited: Inverse Problems, Line
Integrals, Integral Equations, and Integro-Differential
Equations                                                  245
W B. J Zimmrman
7.1 Introduction                                           245
"7.2 Summary                                               290
References                                                 290
8   Modeling of Multi-Phase Flow Using the Level Set Method   293
K. B. Deshpande and W B. J. Zimmeman
8.1 Introduction                                           293
8 2 Governing Equations of the Level Set Method            295
8.3 Curvature Analysist: Methodology                       297
8.4 Results and Discussion                                 297
8.4 1 Coalescence of Two Axisymmetric Drops           298
8.4.2 Coalescence of Acoustically Suspended Drops     304
8 4.3 Coalescence Between Two Drops Approaching Each
Other                                            307
8.4.4 Multi-Body Coalescence                          309
8.5 Summary                                                310
Acknowledgements                                           310
References                                                 310
9   Electrokinetic Flow                                       313
WF. B. J. Zimmerman and J. M  acinnes
9.1 Introduction                                           313
9.2 Weak Boundary Constraints: Revisiting ECT              314
9.3 Electrokinetic Flow                                    319
9.3.1 Background                                      319
9.3.2 Problem Set Up                                  320
9.3.3 FEMLAB Implementation                           321
9 3.4 Links to Physical Boundaries                    327
9.4 Summ ary                                               349
Acknowledgements                                           349
References                                                 349



Library of Congress subject headings for this publication: Manufacturing processes Computer simulation, Mathematical optimization, Finite element method