Loading...Process Modelling and Simulation with Finite Element Methods
William B. J. Zimmerman
University of Sheffield, UK
CONTENTS
About the Author V
Foreword vii
Introduction to FEMLAB
W. B. J. Zimmerman
0.1 Overview of the Book
0.2 An Example from the Model Library
0.2.1 k-&Modelof a Turbulent Static Mixer
0.2.2 Why the Tour of k-EModel of a Turbulent Static
Mixer?
0.3 Chapter Synopsis
References
1 FEMLAB and the Basics of Numerical Analysis
W. B. J.Zimmerman
1.1 Introduction
1.2 Method 1: Root Finding
1.2.1 Root Finding: A Simple Application of the FEMLAB
Nonlinear Solver
1.2.2 Root Finding: Application to Flash Distillation
1.3 Method 2: Numerical Integration by Marching
1.3.1 Numerical Integration: A Simple Example
1.3.2 Numerical Integration: Tubular Reactor Design
1.4 Method 3: Numerical Integration of Ordinary Differential
Equations
1.5 Method 4: Linear Systems Analysis
1.6 Summary
References
Heat Transfer in a Nonuniform Medium
2 Partial Differential Equations and the Finite Element Method
W. B. J. Zimmerman and B. N. Hewakandamby
2.1 Introduction
2.1.1 Poisson’s Equation: An Elliptic PDE
2.1.2 The Diffusion Equation: A Parabolic PDE
2.1.3 The Wave Equation: A Hyperbolic PDE
ixX Process Modelling and Simulation with Finite Element Methods
2.1.4 Boundary Conditions
2.1.5 Basic Elements
2.2 summary
References
3 Multiphysics
W. B. J. Zimmerman
3.1 Introduction
3.2 Buoyant Convection.
3.3 Unsteady Response of a Nonlinear Tubular Reactor
3.4 Heterogeneous Reaction in a Porous Catalyst Pellet
3.5 Discussion
References
4 Extended Multiphysics
W. B. J. Zimmerman, P. 0.Mchedlov-Petrossyan and
G. A. Khomenko
4.1 Introduction
4.2 Heterogeneous Reaction in a Fixed Bed with Premixed Feed
4.3 Primacy of the Buffer Tank
4.4 Linking the 2-D Buffer Tank to the 1-DHeterogeneous Reactor
4.5 Bioreactor Kinetics
4.6 Discussion
References
5 Simulation and NonlinearDynamics
W.B. J. Zimmerman
5.1 Introduction
5.2 Rayleigh-Benard Convection
5.2.1 Heating from Above
5.2.2 Heating from Below
5.2.3 Agreement with Thin Layer Theory
5.3 Viscous Fingering Instabilities
5.3.1 Streamfunction-Vorticity Model with Periodic BCs
5.4 Summary
References
6 Geometric Continuation
W.B. J. Zimmerman and A. F. Routh
6.1 Introduction
6.2 Stationary Geometric Continuation: Pressure Drop in a
Channel with an Orifice Plate
217Contents xi
6.3 Transient Geometric Continuation: Film Drying
6.4 Summary
6.5 End Note: Solver Parameters for Problems with Pointwise
Weak Terms
References
7 Coupling Variables Revisited: Inverse Problems, Line
Integrals,Integral Equations, and Integro-Differential
Equations
W. B. J. Zimmerman
7.1 Introduction
7.2 Summary
References
8 Modeling of Multi-PhaseFlow Using the Level Set Method
K. B. Deshpande and W.B. J. Zimmerman
8.1 Introduction
8.2 Governing Equations of the Level Set Method
8.3 Curvature Analysist: Methodology
8.4 Results and Discussion
8.4.1 Coalescence of Two Axisymetric Drops
8.4.2 Coalescence of Acoustically Suspended Drops
8.4.3 Coalescence Between Two Drops Approaching Each
Other
8.4.4 Multi-Body Coalescence
8.5 Summary
Acknowledgements
References
9 ElectrokineticFlow
W.B. J. Zimmerman and J. M. Macinnes
9.1 Introduction
9.2 Weak Boundary Constraints: Revisiting ECT
9.3 Electrokinetic Flow
9.3.1 Background
9.3.2 Problem Set Up
9.3.3 FEMLAB Implementation
9.3.4 Links to Physical Boundaries
9.4 Summary
Acknowledgements
References
349xii Process Modelling and Simulation with Finite Element Methods
Appendix: A MATLABEEMLAB Primer for Vector Calculus
W. B. J. Zimmerman and J. M. Rees
A.1 Review of Vectors
A.1.1 Representation of Vectors
A. 1.2 Scalar Products, Matrix Multiplication, Unit Vectors,
and Vector Products
A.2 Arrays: Simple Arrays, Cell Arrays, and Structures
A.3 Scalar and Vector Fields: MATLAB Function
Representations
A.4 Differentiation in Multivariable Calculus
A.4.1 The Gradient of a Scalar Field
A.4.2 Derivatives of Vector Fields
A S End Note: Platform Dependence of Meshes
Index 37
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