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Finite Analytic Method in Flows and Heat Transfer - R. A. Bernatz

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Finite Analytic Method in Flows and Heat Transfer

Name: Finite Analytic Method in Flows and Heat Transfer
Brand: Taylor & Francis Inc
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By: R. A. Bernatz

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Hardcover | 12 September 2000 | Edition Number 1

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Hardcover
352 Pages

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22.9 x 15.2 x 2.54

Hardcover

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This work offers systematic coverage of the knowledge needed for numerical computation of fluid flows and heat transfer in five comprehensive parts. Part One provides the reader with a brief history of computational machinary and a presentation of the governing equations for fluid flows and heat transfer. Part Two is devoted to the principles of the finite analytic method and its development for various types of equations. Part Three concentrates on methods of coordinate generation for applications in complex domains. Part Four presents various schemes for accomplishing tasks specified in part three, and Part Five gives the reader a wide variety of problems to solve.

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You Can Find This Book In

Non-Fiction Engineering & Technology Mechanical Engineering & Materials Mechanical Engineering Mathematics Calculus & Mathematical Analysis Biochemical Engineering Technology in General Maths for Engineers Science Physics Materials & States of Matter

Condensed Matter Physics including Liquid State & Solid State Physics Thermodynamics & Heat Science in General Maths for Scientists Materials Science Mechanics of Fluids

Preface	p. xvii
Introduction to Computational Fluid Dynamics	p. 1
Introduction	p. 4
Methods of Prediction	p. 4
Numerical Methods	p. 5
Purpose and Outline	p. 6
Governing Equations	p. 7
Stokes-Fourier Postulates	p. 7
The Navier-Stokes and Energy Equations	p. 8
Compressible Flows	p. 8
Incompressible Flows	p. 9
Vorticity and Stream Function	p. 9
Non-dimensional Governing Equations	p. 10
Turbulent Navier-Stokes and Energy Equations	p. 11
Averaging Processes	p. 11
Averaged Turbulence Equations	p. 14
Turbulence Transport Equations	p. 15
Turbulence Closure	p. 18
First-Order Closure (Zero Equation Model)	p. 18
Second-Order Closure	p. 19
Progress in Turbulence Modeling	p. 21
Second-Order Turbulence Closure Models	p. 21
Modifications of Second-Order Closure Models	p. 23
Numerical Considerations in the Near-Wall Region	p. 24
Overview and Areas for Future Work	p. 26
Classification of PDEs	p. 28
Terminology	p. 28
First-Order Equations and Characteristics	p. 28
Second-Order Equations and Characteristics	p. 32
Well-Posed Problems	p. 35
Well-Posed Problems	p. 35
Example of Existence	p. 35
Example of Uniqueness	p. 36
Example of Instability	p. 37
Existence and Physical Problems	p. 37
Uniqueness and the Downstream Condition	p. 39
Some Improperly Posed Problems	p. 40
Numerical Methods	p. 41
Grid Generation	p. 42
Numerical Methods	p. 42
Finite Difference Method	p. 42
Finite Element Method	p. 44
Finite Analytic Method	p. 45
The Finite Difference Method	p. 47
Discretization	p. 47
Central, Backward and Forward Differences	p. 49
Unsteady, One-Dimensional Heat Equation	p. 52
Error and Stability	p. 55
Error Types	p. 55
Stability	p. 55
Two-Dimensional Heat Equation	p. 56
Exercises for Part I	p. 58
The Finite Analytic Method	p. 62
Basic Principles	p. 65
The Transport Equation	p. 65
FA Fundamentals	p. 66
The One-Dimensional Case	p. 69
The One-Dimensional Transport Equation	p. 69
Finite Analytic Solution	p. 70
Hybrid Finite Analytic Solution	p. 72
FA and FD Coefficient Comparison	p. 72
Burgers' Equation	p. 76
The Two-Dimensional Case	p. 78
The Two-Dimensional Transport Equation	p. 78
FA Solution on Uniform Grids	p. 80
The Poisson Equation	p. 85
FA Solution for Nonuniform Grids	p. 85
Heat Transfer in a Driven Cavity	p. 88
The Three-Dimensional Case	p. 93
Three-Dimensional Transport Equation	p. 93
FA 27-Point Solution for Uniform Grids	p. 96
FA Formulation on Nonuniform Grids	p. 100
The 19-Point FA Formula	p. 105
Analysis of 19- and 27-point FA Schemes	p. 108
11-Point FA Formula	p. 111
FA Solution of 3D Cavity Flow	p. 113
Stability and Convergence	p. 118
Three Operators	p. 118
Consistency of the FA Solution	p. 119
Stability and Convergence	p. 125
Stability	p. 125
Convergence	p. 129
Hyperbolic PDEs	p. 130
Hyperbolic Equations	p. 130
Method of Characteristics	p. 131
FA Method	p. 133
Supersonic Flow in a 2D Channel	p. 136
Explicit Finite Analytic Method	p. 141
Convection Dominated Transport Equation	p. 141
Analytic Solution	p. 143
FA Solution	p. 143
Approximating the Initial Condition	p. 145
Explicit Finite Analytic Scheme	p. 146
EFAS Solution for a Single Equation	p. 147
Exercises for Part II	p. 150
Numerical Grid Generation	p. 152
Introduction to Grid Generation	p. 155
Objectives and Principles	p. 156
Mathematical Framework	p. 157
Standard Coordinate Systems	p. 159
Algebraic Methods	p. 161
Bilinear Map	p. 161
Transfinite Interpolation	p. 162
Differential Coordinate Systems	p. 163
Conformal Maps	p. 164
Elliptic Grid Generation	p. 166
Other Differential Methods	p. 166
Adaptive and Multilevel Methods	p. 167
Adaptive Grids	p. 168
Multilevel Methods	p. 169
Elliptic Grid Generation	p. 173
Harmonic Functions	p. 173
Average Value	p. 174
Maximum and Minimum Principle	p. 175
Simple Elliptic Generator	p. 176
Winslow Generator	p. 178
Poisson Generator	p. 179
Qualitative Analysis	p. 180
Control Functions	p. 182
Equations in [xi] and [eta] Coordinates	p. 187
Derivative Transformations	p. 187
Transformed Equations	p. 189
The Continuity Equation	p. 189
The Transport Equation	p. 190
Diagonal Cartesian Method	p. 192
Current Methods	p. 192
Diagonal Cartesian Method	p. 194
Automatic Boundary Approximation	p. 194
Boundary Point Selection	p. 195
Accuracy Considerations	p. 198
Relative Length Error E1	p. 198
Average Normal Distance E2	p. 200
Two-dimensional Example	p. 201
Three-dimensional Approximations	p. 201
Three-dimensional Example	p. 201
FA Method on DC Coordinates	p. 205
5-Point FA Scheme for Uniform Grids	p. 205
5-Point FA Scheme for Nonuniform Grids	p. 209
Three-Dimensional Case	p. 211
Exercises for Part III	p. 214
Computational Considerations	p. 216
Velocity, Pressure and Staggered Grids	p. 219
The Checkerboard Problem	p. 219
The SIMPLE Algorithm	p. 220
The SIMPLEC Algorithm	p. 225
The SIMPLER Algorithm	p. 226
The PISO Algorithm	p. 227
Convergence Criteria	p. 229
Performance Summary	p. 230
Nonstaggered Grid Methods	p. 231
Pressure Weighted Interpolation Method	p. 231
Poisson Pressure Equation Method	p. 236
Momentum Weighted Interpolation Method	p. 237
Method Comparisons	p. 238
Boundary Conditions	p. 240
Staggered Grids	p. 240
Nonstaggered Grids	p. 241
Cell-Vertex Nodes	p. 241
Cell-Centered Nodes	p. 244
PPEM	p. 245
Ghost Boundary Nodes	p. 246
2D Diagonal Cartesian Method	p. 248
Ghost Boundary Node Method	p. 248
Diagonal Surface Nodes	p. 248
Velocity Boundary Conditions	p. 254
Exercises for Part IV	p. 255
Applications of the FA Method	p. 256
Turbulent Flows	p. 259
Laminar Applications	p. 260
Fluid Dynamics of Disc Valves	p. 260
Mathematical Model	p. 260
Governing Equations	p. 260
Boundary Conditions	p. 261
Results and Discussion	p. 261
Turbulent Heat Transfer	p. 267
Laminar Applications	p. 267
Two-Dimensional Sea Breeze	p. 268
Introduction	p. 268
Mathematical Model	p. 270
Model Equations	p. 270
Initial and Boundary Conditions	p. 271
Results and Discussion	p. 272
Complex Domain Flows	p. 276
Unsaturated Porous Media	p. 276
Mathematical Model	p. 277
Results and Discussion	p. 279
Conjugate Heat Transfer	p. 286
Design of a Compact Heat Exchanger	p. 286
Mathematical Model	p. 289
Results and Discussion	p. 290
The One-Dimensional Case	p. 295
The Two-Dimensional Case	p. 303
Table of Contents provided by Syndetics. All Rights Reserved.

Finite Analytic Method in Flows and Heat Transfer

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Hardcover

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