Finite analytic method in flows and heat transfer

General Remarks. Governing Equations. Classification of Differential Equations. Well-Posed Problems. Numerical Methods. The Finite DIfference Method. Basic Principles. The One-Dimensional Case. The Two-Dimensional Case. The Three-Dimensional Case. Stability and Convergence. Hyperbolic PDEs. Explicit Finite Analytic Method. Introduction to Grid Generation. Elliptic Grid Generation. Equations in E and n Coordinates. Diagonal Cartesian Method. FA Method on Diagonal Cartesian Coordinates. Solving Momentum and Continuity. Non-Staggered Grid Methods. Boundary Conditions. Laminar Flows. Laminar Convective Heat Transfer. Turbulent Flows. Turbulent Convective Heat Transfer. Complex Flows. Conjugate Heat Transfer. Appendix A: The One-Dimensional Case. Appendix B: The Two-Dimensional Case. Appendix C: FA 2-D Laminar Code.;This book contains the fundamental development of the finite analytic method and gives a systematic coverage of knowledge needed for numerical computation of fluid flows and heat transfer. It will be helpful to many including graduate students studying computational fluid dynamics and heat transfer. Cover......Page 1 Half Title......Page 2 Title Page......Page 4 Copyright Page......Page 5 Table of Contents......Page 6 List of Figures......Page 12 List of Tables......Page 16 Preface......Page 18 I: Introduction to Computational Fluid Dynamics......Page 22 1.1: Methods of Prediction......Page 25 1.2: Numerical Methods......Page 26 1.3: Purpose and Outline......Page 27 2.1: Stokes-Fourier Postulates......Page 28 2.2.1: Compressible Flows......Page 29 2.2.3: Vorticity and Stream Function......Page 30 2.2.4: Non-dimensional Governing Equations......Page 31 2.3.1: Averaging Processes......Page 32 2.3.2: Averaged Turbulence Equations......Page 35 2.3.3: Turbulence Transport Equations......Page 36 2.4.1: First-Order Closure (Zero Equation Model)......Page 39 2.4.2: Second-Order Closure......Page 40 2.5.1: Second-Order Turbulence Closure Models......Page 42 2.5.2: Modifications of Second-Order Closure Models......Page 44 2.5.3: Numerical Considerations in the Near-Wall Region......Page 45 2.5.4: Overview and Areas for Future Work......Page 47 3.2: First-Order Equations and Characteristics......Page 49 3.3: Second-Order Equations and Characteristics......Page 53 4.1.1: Example of Existence......Page 56 4.1.2: Example of Uniqueness......Page 57 4.2: Existence and Physical Problems......Page 58 4.3: Uniqueness and the Downstream Condition......Page 60 4.4: Some Improperly Posed Problems......Page 61 Chapter 5: Numerical Methods......Page 62 5.2.1: Finite Difference Method......Page 63 5.2.2: Finite Element Method......Page 65 5.2.3: Finite Analytic Method......Page 66 6.1: Discretization......Page 68 6.2: Central, Backward and Forward Differences......Page 70 6.3: Unsteady, One-Dimensional Heat Equation......Page 73 6.4.2: Stability......Page 76 6.5: Two-Dimensional Heat Equation......Page 77 6.6: Exercises for Part I......Page 79 II: The Finite Analytic Method......Page 83 7.1: The Transport Equation......Page 86 7.2: FA Fundamentals......Page 87 8.1: The One-Dimensional Transport Equation......Page 90 8.2: Finite Analytic Solution......Page 91 8.4: FA and FD Coefficient Comparison......Page 93 8.5: Burgers' Equation......Page 97 9.1: The Two-Dimensional Transport Equation......Page 99 9.2: FA Solution on Uniform Grids......Page 101 9.4: FA Solution for Nonuniform Grids......Page 106 9.5: Heat Transfer in a Driven Cavity......Page 109 10.1: Three-Dimensional Transport Equation......Page 114 10.2: FA 27-Point Solution for Uniform Grids......Page 117 10.3: FA Formulation on Nonuniform Grids......Page 121 10.4: The 19-Point FA Formula......Page 126 10.5: Analysis of 19- and 27-point FA Schemes......Page 129 10.6: 11-Point FA Formula......Page 132 10.7: FA Solution of 3D Cavity Flow......Page 134 11.1: Three Operators......Page 139 11.2: Consistency of the FA Solution......Page 140 11.3.1: Stability......Page 146 11.3.2: Convergence......Page 150 12.1: Hyperbolic Equations......Page 151 12.2: Method of Characteristics......Page 152 12.3: FA Method......Page 154 12.4: Supersonic Flow in a 2D Channel......Page 157 13.1: Convection Dominated Transport Equation......Page 162 13.3: FA Solution......Page 164 13.3.1: Approximating the Initial Condition......Page 166 13.3.2: Explicit Finite Analytic Scheme......Page 167 13.4: EFAS Solution for a Single Equation......Page 168 13.5: Exercises for Part II......Page 171 III: Numerical Grid Generation......Page 173 Chapter 14: Introduction to Grid Generation......Page 176 14.1: Objectives and Principles......Page 177 14.2: Mathematical Framework......Page 178 14.3: Standard Coordinate Systems......Page 180 14.4.1: Bilinear Map......Page 182 14.4.2: Transfinite Interpolation......Page 183 14.5: Differential Coordinate Systems......Page 184 14.5.1: Conformal Maps......Page 185 14.5.3: Other Differential Methods......Page 187 14.6: Adaptive and Multilevel Methods......Page 188 14.6.1: Adaptive Grids......Page 189 14.6.2: Multilevel Methods......Page 190 15.1: Harmonic Functions......Page 194 15.1.1: Average Value......Page 195 15.1.2: Maximum and Minimum Principle......Page 196 15.2: Simple Elliptic Generator......Page 197 15.3: Winslow Generator......Page 199 15.4: Poisson Generator......Page 200 15.4.1: Qualitative Analysis......Page 201 15.4.2: Control Functions......Page 203 16.1: Derivative Transformations......Page 208 16.2.1: The Continuity Equation......Page 210 16.2.2: The Transport Equation......Page 211 17.1: Current Methods......Page 213 17.2.1: Automatic Boundary Approximation......Page 215 17.2.2: Boundary Point Selection......Page 216 17.3.1: Relative Length Error E1......Page 219 17.3.2: Average Normal Distance E2......Page 221 17.6: Three-dimensional Example......Page 222 18.1: 5-Point FA Scheme for Uniform Grids......Page 226 18.2: 5-Point FA Scheme for Nonuniform Grids......Page 230 18.3: Three-Dimensional Case......Page 232 18.4: Exercises for Part III......Page 235 IV: Computational Considerations......Page 237 19.1: The Checkerboard Problem......Page 240 19.2: The SIMPLE Algorithm......Page 241 19.3: The SIMPLEC Algorithm......Page 246 19.4: The SIMPLER Algorithm......Page 247 19.5: The PISO Algorithm......Page 248 19.6: Convergence Criteria......Page 250 19.7: Performance Summary......Page 251 20.1: Pressure Weighted Interpolation Method......Page 252 20.2: Poisson Pressure Equation Method......Page 257 20.3: Momentum Weighted Interpolation Method......Page 258 20.4: Method Comparisons......Page 259 21.1: Staggered Grids......Page 261 21.2.1: Cell-Vertex Nodes......Page 262 21.2.2: Cell-Centered Nodes......Page 265 21.2.3: PPEM......Page 266 21.2.4: Ghost Boundary Nodes......Page 267 21.3.2: Diagonal Surface Nodes......Page 269 21.3.3: Velocity Boundary Conditions......Page 275 21.4: Exercises for Part IV......Page 276 V: Applications of the FA Method......Page 277 Chapter 22: Turbulent Flows......Page 280 22.3.1: Governing Equations......Page 281 22.4: Results and Discussion......Page 282 23.1: Laminar Applications......Page 288 23.2.1: Introduction......Page 289 23.3.1: Model Equations......Page 291 23.3.2: Initial and Boundary Conditions......Page 292 23.4: Results and Discussion......Page 293 24.1: Unsaturated Porous Media......Page 297 24.2: Mathematical Model......Page 298 24.3: Results and Discussion......Page 300 25.1: Design of a Compact Heat Exchanger......Page 307 25.2: Mathematical Model......Page 310 25.3: Results and Discussion......Page 311 A: The One-Dimensional Case......Page 316 B: The Two-Dimensional Case......Page 324 Bibliography......Page 332 Index......Page 348 Disclaimer These Books Are For A Mature Audience And Contain Adult Language, Mature Scenes, And Graphic Violence. Some Imagery And Descriptions May Be Disturbing For Sensitive Readers. Reader Discretion Is Advised. About Modi Indorum Is Book One In The Fibonacci Series, A Crime Dark Thriller Story About A Drug Organization, A Designer Heroin, And The People Involved. It Is Also The First Book Of The Jardine Trilogy, A Novel About A Middle-aged Rookie Detective With Ptsd, Her Love Interest And Partner (who's Also A Double Agent), And A Hacker-turned-serial Killer Who Claims To Be Protecting Her. Book Description 55. That's The Number Carved On A Sea Shell In The Hand Of A Dead Heroin Addict When Detective Ameena Aj Jardine Meets D.e.a. Agent Tony Aserbbo On Her First Solo Assignment. The Death Is Ruled An Overdose--nothing Unusual Considering The Heroin Epidemic Plaguing New England. 34. That's The Number Of Daisies In The Hand Of Another Dead Heroin Addict A Year Later When The Crime Scene Brings Aj And Tony Back Together For The First Time Since Their Relationship Dissolved. 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The Rest Of The Story Will Be Told And Revealed In Future Books Through The Serial Killer's (the Copernicus Duology - Coming In 2018) And Tony's (the Aserbbo Duology) Perspectives.