Page 10 - Process Modelling and Simulation With Finite Element Methods
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CONTENTS
About the Author V
Foreword vii
Introduction to FEMLAB 1
W. B. J. Zimmerman
0.1 Overview of the Book 1
0.2 An Example from the Model Library 11
0.2.1 k-&Model of a Turbulent Static Mixer 12
0.2.2 Why the Tour of k-E Model of a Turbulent Static
Mixer? 14
0.3 Chapter Synopsis 16
References 22
1 FEMLAB and the Basics of Numerical Analysis 23
W. B. J. Zimmerman
1.1 Introduction 23
1.2 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
2 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
ix
