A. J. Baker
Optimal Modified Continuous Galerkin CFD
A. J. Baker
Optimal Modified Continuous Galerkin CFD
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Covers the theory and applications of using weak form theory in incompressible fluid-thermal sciences
Giving you a solid foundation on the Galerkin finite-element method (FEM), this book promotes the use of optimal modified continuous Galerkin weak form theory to generate discrete approximate solutions to incompressible-thermal Navier-Stokes equations. The book covers the topic comprehensively by introducing formulations, theory and implementation of FEM and various flow formulations.
The author first introduces concepts, terminology and methodology related to the topic before covering…mehr
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Covers the theory and applications of using weak form theory in incompressible fluid-thermal sciences
Giving you a solid foundation on the Galerkin finite-element method (FEM), this book promotes the use of optimal modified continuous Galerkin weak form theory to generate discrete approximate solutions to incompressible-thermal Navier-Stokes equations. The book covers the topic comprehensively by introducing formulations, theory and implementation of FEM and various flow formulations.
The author first introduces concepts, terminology and methodology related to the topic before covering topics including aerodynamics; the Navier-Stokes Equations; vector field theory implementations and large eddy simulation formulations.
Introduces and addresses many different flow models (Navier-Stokes, full-potential, potential, compressible/incompressible) from a unified perspective
Focuses on Galerkin methods for CFD beneficial for engineering graduate students and engineering professionals
Accompanied by a website with sample applications of the algorithms and example problems and solutions
This approach is useful for graduate students in various engineering fields and as well as professional engineers.
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Giving you a solid foundation on the Galerkin finite-element method (FEM), this book promotes the use of optimal modified continuous Galerkin weak form theory to generate discrete approximate solutions to incompressible-thermal Navier-Stokes equations. The book covers the topic comprehensively by introducing formulations, theory and implementation of FEM and various flow formulations.
The author first introduces concepts, terminology and methodology related to the topic before covering topics including aerodynamics; the Navier-Stokes Equations; vector field theory implementations and large eddy simulation formulations.
Introduces and addresses many different flow models (Navier-Stokes, full-potential, potential, compressible/incompressible) from a unified perspective
Focuses on Galerkin methods for CFD beneficial for engineering graduate students and engineering professionals
Accompanied by a website with sample applications of the algorithms and example problems and solutions
This approach is useful for graduate students in various engineering fields and as well as professional engineers.
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Produktdetails
- Produktdetails
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 576
- Erscheinungstermin: 5. Mai 2014
- Englisch
- Abmessung: 246mm x 168mm x 33mm
- Gewicht: 1016g
- ISBN-13: 9781119940494
- ISBN-10: 1119940494
- Artikelnr.: 38025042
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 576
- Erscheinungstermin: 5. Mai 2014
- Englisch
- Abmessung: 246mm x 168mm x 33mm
- Gewicht: 1016g
- ISBN-13: 9781119940494
- ISBN-10: 1119940494
- Artikelnr.: 38025042
A. J. Baker, The University of Tennessee, USA Professor Baker is Professor Emeritus in both the Engineering Science Department and the Computational Mechanics Department at the University of Tennessee. Prior to this he was Director of UT CFD Laboratory at the University of Tennessee. He is a Fellow of International Association for Computational Mechanics (IACM) and the US Association for Computational Mechanics (USACM) as well as being an Associate Fellow of the American Institute of Aeronautics and Astronautics (AIAA). Professor Baker has devised many courses on FEA-related topics during his career and has also written multiple books and journal articles.
Preface xiii About the Author xvii Notations xix 1 Introduction 1 1.1 About
This Book 1 1.2 The Navier-Stokes Conservation Principles System 2 1.3
Navier-Stokes PDE System Manipulations 5 1.4 Weak Form Overview 7 1.5 A
Brief History of Finite Element CFD 9 1.6 A Brief Summary 11 References 12
2 Concepts, terminology, methodology 15 2.1 Overview 15 2.2 Steady DE Weak
Form Completion 16 2.3 Steady DE GWSN Discrete FE Implementation 19 2.4 PDE
Solutions, Classical Concepts 27 2.5 The Sturm-Liouville Equation,
Orthogonality, Completeness 30 2.6 Classical Variational Calculus 33 2.7
Variational Calculus, Weak Form Duality 36 2.8 Quadratic Forms, Norms,
Error Estimation 38 2.9 Theory Illustrations for Non-Smooth, Nonlinear Data
40 2.10 Matrix Algebra, Notation 44 2.11 Equation Solving, Linear Algebra
46 2.12 Krylov Sparse Matrix Solver Methodology 53 2.13 Summary 54
Exercises 54 References 56 3 Aerodynamics I: Potential flow, GWSh theory
exposition, transonic flow mPDE shock capturing 59 3.1 Aerodynamics, Weak
Interaction 59 3.2 Navier-Stokes Manipulations for Aerodynamics 60 3.3
Steady Potential Flow GWS 62 3.4 Accuracy, Convergence, Mathematical
Preliminaries 66 3.5 Accuracy, Galerkin Weak Form Optimality 68 3.6
Accuracy, GWSh Error Bound 71 3.7 Accuracy, GWSh Asymptotic Convergence 73
3.8 GWSh Natural Coordinate FE Basis Matrices 76 3.9 GWSh Tensor Product FE
Basis Matrices 82 3.10 GWSh Comparison with Laplacian FD and FV Stencils 87
3.11 Post-Processing Pressure Distributions 90 3.12 Transonic Potential
Flow, Shock Capturing 92 3.13 Summary 96 Exercises 98 References 99 4
Aerodynamics II: boundary layers, turbulence closure modeling, parabolic
Navier-Stokes 101 4.1 Aerodynamics, Weak Interaction Reprise 101 4.2
Navier-Stokes PDE System Reynolds Ordered 102 4.3 GWSh, n= 2
Laminar-Thermal Boundary Layer 104 4.4 GWSh + thetaTS BL Matrix Iteration
Algorithm 108 4.5 Accuracy, Convergence, Optimal Mesh Solutions 111 4.6
GWSh +thetaTS Solution Optimality, Data Influence 115 4.7 Time Averaged NS,
Turbulent BL Formulation 116 4.8 Turbulent BL GWSh+ thetaTS, Accuracy,
Convergence 120 4.9 GWSh+ thetaTS BL Algorithm, TKE Closure Models 123 4.10
The Parabolic Navier-Stokes PDE System 129 4.11 GWSh +thetaTS Algorithm for
PNS PDE System 134 4.12 GWSh +thetaTS k=1 NC Basis PNS Algorithm 137 4.13
Weak Interaction PNS Algorithm Validation 141 4.14 Square Duct PNS
Algorithm Validation 147 4.15 Summary 148 Exercises 155 References 157 5
The Navier-Stokes Equations: theoretical fundamentals; constraint, spectral
analyses, mPDE theory, optimal Galerkin weak forms 159 5.1 The
Incompressible Navier-Stokes PDE System 159 5.2 Continuity Constraint,
Exact Enforcement 160 5.3 Continuity Constraint, Inexact Enforcement 164
5.4 The CCM Pressure Projection Algorithm 166 5.5 Convective Transport,
Phase Velocity 168 5.6 Convection-Diffusion, Phase Speed Characterization
170 5.7 Theory for Optimal mGWSh+ thetaTS Phase Accuracy 177 5.8 Optimally
Phase Accurate mGWSh + thetaTS in n Dimensions 185 5.9 Theory for Optimal
mGWSh Asymptotic Convergence 193 5.10 The Optimal mGWSh ? thetaTS k ? 1
Basis NS Algorithm 201 5.11 Summary 203 Exercises 206 References 208 6
Vector Field Theory Implementations: vorticity-streamfunction,
vorticity-velocity formulations 211 6.1 Vector Field Theory NS PDE
Manipulations 211 6.2 Vorticity-Streamfunction PDE System, n= 2 213 6.3
Vorticity-Streamfunction mGWSh Algorithm 214 6.4 Weak Form Theory
Verification, GWSh/mGWSh 219 6.5 Vorticity-Velocity mGWSh Algorithm, n= 3
228 6.6 Vorticity-Velocity GWSh+ thetaTS Assessments, n= 3 233 6.7 Summary
243 Exercises 246 References 247 7 Classic State Variable Formulations:
GWS/mGWSh+thetaTS algorithms for Navier-Stokes; accuracy, convergence,
validation, BCs, radiation, ALE formulation 249 7.1 Classic State Variable
Navier-Stokes PDE System 249 7.2 NS Classic State Variable mPDE System 251
7.3 NS Classic State Variable mGWSh+ thetaTS Algorithm 252 7.4 NS mGWSh
+thetaTS Algorithm Discrete Formation 254 7.5 mGWSh+ thetaTS Algorithm
Completion 258 7.6 mGWSh+ thetaTS Algorithm Benchmarks, n=2 260 7.7 mGWSh+
thetaTS Algorithm Validations, n= 3 268 7.8 Flow Bifurcation, Multiple
Outflow Pressure BCs 282 7.9 Convection/Radiation BCs in GWSh+ thetaTS 283
7.10 Convection BCs Validation 288 7.11 Radiosity, GWSh Algorithm 295 7.12
Radiosity BC, Accuracy, Convergence, Validation 298 7.13 ALE
Thermo-Solid-Fluid-Mass Transport Algorithm 302 7.14 ALE GWSh +thetaTS
Algorithm LISI Validation 304 7.15 Summary 310 Exercises 317 References 318
8 Time Averaged Navier-Stokes: mGWSh+thetaTS algorithm for RaNS, Reynolds
stress tensor closure models 319 8.1 Classic State Variable RaNS PDE System
319 8.2 RaNS PDE System Turbulence Closure 321 8.3 RaNS State Variable mPDE
System 323 8.4 RaNS mGWSh+thetaTS Algorithm Matrix Statement 325 8.5 RaNS
mGWSh + thetaTS Algorithm, Stability, Accuracy 331 8.6 RaNS Algorithm BCs
for Conjugate Heat Transfer 337 8.7 RaNS Full Reynolds Stress Closure PDE
System 341 8.8 RSM Closure mGWSh +thetaTS Algorithm 345 8.9 RSM Closure
Model Validation 347 8.10 Geologic Borehole Conjugate Heat Transfer 348
8.11 Summary 358 Exercises 363 References 364 9 Space Filtered
Navier-Stokes: GWSh/mGWSh+thetaTS for space filtered Navier-Stokes,
modeled, analytical closure 365 9.1 Classic State Variable LES PDE System
365 9.2 Space Filtered NS PDE System 366 9.3 SGS Tensor Closure Modeling
for LES 368 9.4 Rational LES Theory Predictions 371 9.5 RLES Unresolved
Scale SFS Tensor Models 376 9.6 Analytical SFS Tensor/Vector Closures 381
9.7 Auxiliary Problem Resolution Via Perturbation Theory 383 9.8 LES
Analytical Closure (arLES) Theory 386 9.9 arLES Theory mGWSh + thetaTS
Algorithm 387 9.10 arLES Theory mGWSh + thetaTS Completion 391 9.11 arLES
Theory Implementation Diagnostics 392 9.12 RLES Theory Turbulent BL
Validation 403 9.13 Space Filtered NS PDE System on Bounded Domains 409
9.14 Space Filtered NS Bounded Domain BCs 410 9.15 ADBC Algorithm
Validation, Space Filtered DE 412 9.16 arLES Theory Resolved Scale BCE
Integrals 420 9.17 Turbulent Resolved Scale Velocity BC Optimal
Omegah-delta 423 9.18 Resolved Scale Velocity DBC Validation 8 Re 430 9.19
arLES O(delta2) State Variable Bounded Domain BCs 430 9.20 Well-Posed arLES
Theory n = 3 Validation 433 9.21 Well-Posed arLES Theory n = 3 Diagnostics
441 9.22 Summary 446 Exercises 455 References 456 10 Summary-VVUQ:
verification, validation, uncertainty quantification 459 10.1 Beyond
Colorful Fluid Dynamics 459 10.2 Observations on Computational Reliability
460 10.3 Solving the Equations Right 461 10.4 Solving the Right Equations
464 10.5 Solving the Right Equations Without Modeling 466 10.6 Solving the
Right Equations Well-Posed 468 10.7 Well-Posed Right Equations Optimal CFD
471 10.8 The Right Closing Caveat 473 References 474 Appendix A: Well-Posed
arLES Theory PICMSS Template 475 Appendix B: Hypersonic Parabolic
Navier-Stokes 483 B.1 High Speed External Aerodynamics 483 B.2 Compressible
Navier-Stokes PDE System 484 B.3 Parabolic Compressible RaNS PDE System 488
B.4 Compressible PRaNS mPDE System Closure 490 B.5 Bow Shock Fitting, PRaNS
State Variable IC 493 B.6 The PRaNS mGWSh+thetaTS Algorithm 496 B.7 PRaNS
mGWSh+thetaTS Algorithm Completion 501 B.8 PRaNS Algorithm IC Generation
505 B.9 PRaNS mGWSh+thetaTS Algorithm Validation 507 B.10 Hypersonic Blunt
Body Shock Trajectory 515 B.11 Shock Trajectory Characteristics Algorithm
521 B.12 Blunt Body PRaNS Algorithm Validation 523 B.13 Summary 527
Exercises 532 References 533 Author Index 535 Subject Index 541
This Book 1 1.2 The Navier-Stokes Conservation Principles System 2 1.3
Navier-Stokes PDE System Manipulations 5 1.4 Weak Form Overview 7 1.5 A
Brief History of Finite Element CFD 9 1.6 A Brief Summary 11 References 12
2 Concepts, terminology, methodology 15 2.1 Overview 15 2.2 Steady DE Weak
Form Completion 16 2.3 Steady DE GWSN Discrete FE Implementation 19 2.4 PDE
Solutions, Classical Concepts 27 2.5 The Sturm-Liouville Equation,
Orthogonality, Completeness 30 2.6 Classical Variational Calculus 33 2.7
Variational Calculus, Weak Form Duality 36 2.8 Quadratic Forms, Norms,
Error Estimation 38 2.9 Theory Illustrations for Non-Smooth, Nonlinear Data
40 2.10 Matrix Algebra, Notation 44 2.11 Equation Solving, Linear Algebra
46 2.12 Krylov Sparse Matrix Solver Methodology 53 2.13 Summary 54
Exercises 54 References 56 3 Aerodynamics I: Potential flow, GWSh theory
exposition, transonic flow mPDE shock capturing 59 3.1 Aerodynamics, Weak
Interaction 59 3.2 Navier-Stokes Manipulations for Aerodynamics 60 3.3
Steady Potential Flow GWS 62 3.4 Accuracy, Convergence, Mathematical
Preliminaries 66 3.5 Accuracy, Galerkin Weak Form Optimality 68 3.6
Accuracy, GWSh Error Bound 71 3.7 Accuracy, GWSh Asymptotic Convergence 73
3.8 GWSh Natural Coordinate FE Basis Matrices 76 3.9 GWSh Tensor Product FE
Basis Matrices 82 3.10 GWSh Comparison with Laplacian FD and FV Stencils 87
3.11 Post-Processing Pressure Distributions 90 3.12 Transonic Potential
Flow, Shock Capturing 92 3.13 Summary 96 Exercises 98 References 99 4
Aerodynamics II: boundary layers, turbulence closure modeling, parabolic
Navier-Stokes 101 4.1 Aerodynamics, Weak Interaction Reprise 101 4.2
Navier-Stokes PDE System Reynolds Ordered 102 4.3 GWSh, n= 2
Laminar-Thermal Boundary Layer 104 4.4 GWSh + thetaTS BL Matrix Iteration
Algorithm 108 4.5 Accuracy, Convergence, Optimal Mesh Solutions 111 4.6
GWSh +thetaTS Solution Optimality, Data Influence 115 4.7 Time Averaged NS,
Turbulent BL Formulation 116 4.8 Turbulent BL GWSh+ thetaTS, Accuracy,
Convergence 120 4.9 GWSh+ thetaTS BL Algorithm, TKE Closure Models 123 4.10
The Parabolic Navier-Stokes PDE System 129 4.11 GWSh +thetaTS Algorithm for
PNS PDE System 134 4.12 GWSh +thetaTS k=1 NC Basis PNS Algorithm 137 4.13
Weak Interaction PNS Algorithm Validation 141 4.14 Square Duct PNS
Algorithm Validation 147 4.15 Summary 148 Exercises 155 References 157 5
The Navier-Stokes Equations: theoretical fundamentals; constraint, spectral
analyses, mPDE theory, optimal Galerkin weak forms 159 5.1 The
Incompressible Navier-Stokes PDE System 159 5.2 Continuity Constraint,
Exact Enforcement 160 5.3 Continuity Constraint, Inexact Enforcement 164
5.4 The CCM Pressure Projection Algorithm 166 5.5 Convective Transport,
Phase Velocity 168 5.6 Convection-Diffusion, Phase Speed Characterization
170 5.7 Theory for Optimal mGWSh+ thetaTS Phase Accuracy 177 5.8 Optimally
Phase Accurate mGWSh + thetaTS in n Dimensions 185 5.9 Theory for Optimal
mGWSh Asymptotic Convergence 193 5.10 The Optimal mGWSh ? thetaTS k ? 1
Basis NS Algorithm 201 5.11 Summary 203 Exercises 206 References 208 6
Vector Field Theory Implementations: vorticity-streamfunction,
vorticity-velocity formulations 211 6.1 Vector Field Theory NS PDE
Manipulations 211 6.2 Vorticity-Streamfunction PDE System, n= 2 213 6.3
Vorticity-Streamfunction mGWSh Algorithm 214 6.4 Weak Form Theory
Verification, GWSh/mGWSh 219 6.5 Vorticity-Velocity mGWSh Algorithm, n= 3
228 6.6 Vorticity-Velocity GWSh+ thetaTS Assessments, n= 3 233 6.7 Summary
243 Exercises 246 References 247 7 Classic State Variable Formulations:
GWS/mGWSh+thetaTS algorithms for Navier-Stokes; accuracy, convergence,
validation, BCs, radiation, ALE formulation 249 7.1 Classic State Variable
Navier-Stokes PDE System 249 7.2 NS Classic State Variable mPDE System 251
7.3 NS Classic State Variable mGWSh+ thetaTS Algorithm 252 7.4 NS mGWSh
+thetaTS Algorithm Discrete Formation 254 7.5 mGWSh+ thetaTS Algorithm
Completion 258 7.6 mGWSh+ thetaTS Algorithm Benchmarks, n=2 260 7.7 mGWSh+
thetaTS Algorithm Validations, n= 3 268 7.8 Flow Bifurcation, Multiple
Outflow Pressure BCs 282 7.9 Convection/Radiation BCs in GWSh+ thetaTS 283
7.10 Convection BCs Validation 288 7.11 Radiosity, GWSh Algorithm 295 7.12
Radiosity BC, Accuracy, Convergence, Validation 298 7.13 ALE
Thermo-Solid-Fluid-Mass Transport Algorithm 302 7.14 ALE GWSh +thetaTS
Algorithm LISI Validation 304 7.15 Summary 310 Exercises 317 References 318
8 Time Averaged Navier-Stokes: mGWSh+thetaTS algorithm for RaNS, Reynolds
stress tensor closure models 319 8.1 Classic State Variable RaNS PDE System
319 8.2 RaNS PDE System Turbulence Closure 321 8.3 RaNS State Variable mPDE
System 323 8.4 RaNS mGWSh+thetaTS Algorithm Matrix Statement 325 8.5 RaNS
mGWSh + thetaTS Algorithm, Stability, Accuracy 331 8.6 RaNS Algorithm BCs
for Conjugate Heat Transfer 337 8.7 RaNS Full Reynolds Stress Closure PDE
System 341 8.8 RSM Closure mGWSh +thetaTS Algorithm 345 8.9 RSM Closure
Model Validation 347 8.10 Geologic Borehole Conjugate Heat Transfer 348
8.11 Summary 358 Exercises 363 References 364 9 Space Filtered
Navier-Stokes: GWSh/mGWSh+thetaTS for space filtered Navier-Stokes,
modeled, analytical closure 365 9.1 Classic State Variable LES PDE System
365 9.2 Space Filtered NS PDE System 366 9.3 SGS Tensor Closure Modeling
for LES 368 9.4 Rational LES Theory Predictions 371 9.5 RLES Unresolved
Scale SFS Tensor Models 376 9.6 Analytical SFS Tensor/Vector Closures 381
9.7 Auxiliary Problem Resolution Via Perturbation Theory 383 9.8 LES
Analytical Closure (arLES) Theory 386 9.9 arLES Theory mGWSh + thetaTS
Algorithm 387 9.10 arLES Theory mGWSh + thetaTS Completion 391 9.11 arLES
Theory Implementation Diagnostics 392 9.12 RLES Theory Turbulent BL
Validation 403 9.13 Space Filtered NS PDE System on Bounded Domains 409
9.14 Space Filtered NS Bounded Domain BCs 410 9.15 ADBC Algorithm
Validation, Space Filtered DE 412 9.16 arLES Theory Resolved Scale BCE
Integrals 420 9.17 Turbulent Resolved Scale Velocity BC Optimal
Omegah-delta 423 9.18 Resolved Scale Velocity DBC Validation 8 Re 430 9.19
arLES O(delta2) State Variable Bounded Domain BCs 430 9.20 Well-Posed arLES
Theory n = 3 Validation 433 9.21 Well-Posed arLES Theory n = 3 Diagnostics
441 9.22 Summary 446 Exercises 455 References 456 10 Summary-VVUQ:
verification, validation, uncertainty quantification 459 10.1 Beyond
Colorful Fluid Dynamics 459 10.2 Observations on Computational Reliability
460 10.3 Solving the Equations Right 461 10.4 Solving the Right Equations
464 10.5 Solving the Right Equations Without Modeling 466 10.6 Solving the
Right Equations Well-Posed 468 10.7 Well-Posed Right Equations Optimal CFD
471 10.8 The Right Closing Caveat 473 References 474 Appendix A: Well-Posed
arLES Theory PICMSS Template 475 Appendix B: Hypersonic Parabolic
Navier-Stokes 483 B.1 High Speed External Aerodynamics 483 B.2 Compressible
Navier-Stokes PDE System 484 B.3 Parabolic Compressible RaNS PDE System 488
B.4 Compressible PRaNS mPDE System Closure 490 B.5 Bow Shock Fitting, PRaNS
State Variable IC 493 B.6 The PRaNS mGWSh+thetaTS Algorithm 496 B.7 PRaNS
mGWSh+thetaTS Algorithm Completion 501 B.8 PRaNS Algorithm IC Generation
505 B.9 PRaNS mGWSh+thetaTS Algorithm Validation 507 B.10 Hypersonic Blunt
Body Shock Trajectory 515 B.11 Shock Trajectory Characteristics Algorithm
521 B.12 Blunt Body PRaNS Algorithm Validation 523 B.13 Summary 527
Exercises 532 References 533 Author Index 535 Subject Index 541
Preface xiii About the Author xvii Notations xix 1 Introduction 1 1.1 About
This Book 1 1.2 The Navier-Stokes Conservation Principles System 2 1.3
Navier-Stokes PDE System Manipulations 5 1.4 Weak Form Overview 7 1.5 A
Brief History of Finite Element CFD 9 1.6 A Brief Summary 11 References 12
2 Concepts, terminology, methodology 15 2.1 Overview 15 2.2 Steady DE Weak
Form Completion 16 2.3 Steady DE GWSN Discrete FE Implementation 19 2.4 PDE
Solutions, Classical Concepts 27 2.5 The Sturm-Liouville Equation,
Orthogonality, Completeness 30 2.6 Classical Variational Calculus 33 2.7
Variational Calculus, Weak Form Duality 36 2.8 Quadratic Forms, Norms,
Error Estimation 38 2.9 Theory Illustrations for Non-Smooth, Nonlinear Data
40 2.10 Matrix Algebra, Notation 44 2.11 Equation Solving, Linear Algebra
46 2.12 Krylov Sparse Matrix Solver Methodology 53 2.13 Summary 54
Exercises 54 References 56 3 Aerodynamics I: Potential flow, GWSh theory
exposition, transonic flow mPDE shock capturing 59 3.1 Aerodynamics, Weak
Interaction 59 3.2 Navier-Stokes Manipulations for Aerodynamics 60 3.3
Steady Potential Flow GWS 62 3.4 Accuracy, Convergence, Mathematical
Preliminaries 66 3.5 Accuracy, Galerkin Weak Form Optimality 68 3.6
Accuracy, GWSh Error Bound 71 3.7 Accuracy, GWSh Asymptotic Convergence 73
3.8 GWSh Natural Coordinate FE Basis Matrices 76 3.9 GWSh Tensor Product FE
Basis Matrices 82 3.10 GWSh Comparison with Laplacian FD and FV Stencils 87
3.11 Post-Processing Pressure Distributions 90 3.12 Transonic Potential
Flow, Shock Capturing 92 3.13 Summary 96 Exercises 98 References 99 4
Aerodynamics II: boundary layers, turbulence closure modeling, parabolic
Navier-Stokes 101 4.1 Aerodynamics, Weak Interaction Reprise 101 4.2
Navier-Stokes PDE System Reynolds Ordered 102 4.3 GWSh, n= 2
Laminar-Thermal Boundary Layer 104 4.4 GWSh + thetaTS BL Matrix Iteration
Algorithm 108 4.5 Accuracy, Convergence, Optimal Mesh Solutions 111 4.6
GWSh +thetaTS Solution Optimality, Data Influence 115 4.7 Time Averaged NS,
Turbulent BL Formulation 116 4.8 Turbulent BL GWSh+ thetaTS, Accuracy,
Convergence 120 4.9 GWSh+ thetaTS BL Algorithm, TKE Closure Models 123 4.10
The Parabolic Navier-Stokes PDE System 129 4.11 GWSh +thetaTS Algorithm for
PNS PDE System 134 4.12 GWSh +thetaTS k=1 NC Basis PNS Algorithm 137 4.13
Weak Interaction PNS Algorithm Validation 141 4.14 Square Duct PNS
Algorithm Validation 147 4.15 Summary 148 Exercises 155 References 157 5
The Navier-Stokes Equations: theoretical fundamentals; constraint, spectral
analyses, mPDE theory, optimal Galerkin weak forms 159 5.1 The
Incompressible Navier-Stokes PDE System 159 5.2 Continuity Constraint,
Exact Enforcement 160 5.3 Continuity Constraint, Inexact Enforcement 164
5.4 The CCM Pressure Projection Algorithm 166 5.5 Convective Transport,
Phase Velocity 168 5.6 Convection-Diffusion, Phase Speed Characterization
170 5.7 Theory for Optimal mGWSh+ thetaTS Phase Accuracy 177 5.8 Optimally
Phase Accurate mGWSh + thetaTS in n Dimensions 185 5.9 Theory for Optimal
mGWSh Asymptotic Convergence 193 5.10 The Optimal mGWSh ? thetaTS k ? 1
Basis NS Algorithm 201 5.11 Summary 203 Exercises 206 References 208 6
Vector Field Theory Implementations: vorticity-streamfunction,
vorticity-velocity formulations 211 6.1 Vector Field Theory NS PDE
Manipulations 211 6.2 Vorticity-Streamfunction PDE System, n= 2 213 6.3
Vorticity-Streamfunction mGWSh Algorithm 214 6.4 Weak Form Theory
Verification, GWSh/mGWSh 219 6.5 Vorticity-Velocity mGWSh Algorithm, n= 3
228 6.6 Vorticity-Velocity GWSh+ thetaTS Assessments, n= 3 233 6.7 Summary
243 Exercises 246 References 247 7 Classic State Variable Formulations:
GWS/mGWSh+thetaTS algorithms for Navier-Stokes; accuracy, convergence,
validation, BCs, radiation, ALE formulation 249 7.1 Classic State Variable
Navier-Stokes PDE System 249 7.2 NS Classic State Variable mPDE System 251
7.3 NS Classic State Variable mGWSh+ thetaTS Algorithm 252 7.4 NS mGWSh
+thetaTS Algorithm Discrete Formation 254 7.5 mGWSh+ thetaTS Algorithm
Completion 258 7.6 mGWSh+ thetaTS Algorithm Benchmarks, n=2 260 7.7 mGWSh+
thetaTS Algorithm Validations, n= 3 268 7.8 Flow Bifurcation, Multiple
Outflow Pressure BCs 282 7.9 Convection/Radiation BCs in GWSh+ thetaTS 283
7.10 Convection BCs Validation 288 7.11 Radiosity, GWSh Algorithm 295 7.12
Radiosity BC, Accuracy, Convergence, Validation 298 7.13 ALE
Thermo-Solid-Fluid-Mass Transport Algorithm 302 7.14 ALE GWSh +thetaTS
Algorithm LISI Validation 304 7.15 Summary 310 Exercises 317 References 318
8 Time Averaged Navier-Stokes: mGWSh+thetaTS algorithm for RaNS, Reynolds
stress tensor closure models 319 8.1 Classic State Variable RaNS PDE System
319 8.2 RaNS PDE System Turbulence Closure 321 8.3 RaNS State Variable mPDE
System 323 8.4 RaNS mGWSh+thetaTS Algorithm Matrix Statement 325 8.5 RaNS
mGWSh + thetaTS Algorithm, Stability, Accuracy 331 8.6 RaNS Algorithm BCs
for Conjugate Heat Transfer 337 8.7 RaNS Full Reynolds Stress Closure PDE
System 341 8.8 RSM Closure mGWSh +thetaTS Algorithm 345 8.9 RSM Closure
Model Validation 347 8.10 Geologic Borehole Conjugate Heat Transfer 348
8.11 Summary 358 Exercises 363 References 364 9 Space Filtered
Navier-Stokes: GWSh/mGWSh+thetaTS for space filtered Navier-Stokes,
modeled, analytical closure 365 9.1 Classic State Variable LES PDE System
365 9.2 Space Filtered NS PDE System 366 9.3 SGS Tensor Closure Modeling
for LES 368 9.4 Rational LES Theory Predictions 371 9.5 RLES Unresolved
Scale SFS Tensor Models 376 9.6 Analytical SFS Tensor/Vector Closures 381
9.7 Auxiliary Problem Resolution Via Perturbation Theory 383 9.8 LES
Analytical Closure (arLES) Theory 386 9.9 arLES Theory mGWSh + thetaTS
Algorithm 387 9.10 arLES Theory mGWSh + thetaTS Completion 391 9.11 arLES
Theory Implementation Diagnostics 392 9.12 RLES Theory Turbulent BL
Validation 403 9.13 Space Filtered NS PDE System on Bounded Domains 409
9.14 Space Filtered NS Bounded Domain BCs 410 9.15 ADBC Algorithm
Validation, Space Filtered DE 412 9.16 arLES Theory Resolved Scale BCE
Integrals 420 9.17 Turbulent Resolved Scale Velocity BC Optimal
Omegah-delta 423 9.18 Resolved Scale Velocity DBC Validation 8 Re 430 9.19
arLES O(delta2) State Variable Bounded Domain BCs 430 9.20 Well-Posed arLES
Theory n = 3 Validation 433 9.21 Well-Posed arLES Theory n = 3 Diagnostics
441 9.22 Summary 446 Exercises 455 References 456 10 Summary-VVUQ:
verification, validation, uncertainty quantification 459 10.1 Beyond
Colorful Fluid Dynamics 459 10.2 Observations on Computational Reliability
460 10.3 Solving the Equations Right 461 10.4 Solving the Right Equations
464 10.5 Solving the Right Equations Without Modeling 466 10.6 Solving the
Right Equations Well-Posed 468 10.7 Well-Posed Right Equations Optimal CFD
471 10.8 The Right Closing Caveat 473 References 474 Appendix A: Well-Posed
arLES Theory PICMSS Template 475 Appendix B: Hypersonic Parabolic
Navier-Stokes 483 B.1 High Speed External Aerodynamics 483 B.2 Compressible
Navier-Stokes PDE System 484 B.3 Parabolic Compressible RaNS PDE System 488
B.4 Compressible PRaNS mPDE System Closure 490 B.5 Bow Shock Fitting, PRaNS
State Variable IC 493 B.6 The PRaNS mGWSh+thetaTS Algorithm 496 B.7 PRaNS
mGWSh+thetaTS Algorithm Completion 501 B.8 PRaNS Algorithm IC Generation
505 B.9 PRaNS mGWSh+thetaTS Algorithm Validation 507 B.10 Hypersonic Blunt
Body Shock Trajectory 515 B.11 Shock Trajectory Characteristics Algorithm
521 B.12 Blunt Body PRaNS Algorithm Validation 523 B.13 Summary 527
Exercises 532 References 533 Author Index 535 Subject Index 541
This Book 1 1.2 The Navier-Stokes Conservation Principles System 2 1.3
Navier-Stokes PDE System Manipulations 5 1.4 Weak Form Overview 7 1.5 A
Brief History of Finite Element CFD 9 1.6 A Brief Summary 11 References 12
2 Concepts, terminology, methodology 15 2.1 Overview 15 2.2 Steady DE Weak
Form Completion 16 2.3 Steady DE GWSN Discrete FE Implementation 19 2.4 PDE
Solutions, Classical Concepts 27 2.5 The Sturm-Liouville Equation,
Orthogonality, Completeness 30 2.6 Classical Variational Calculus 33 2.7
Variational Calculus, Weak Form Duality 36 2.8 Quadratic Forms, Norms,
Error Estimation 38 2.9 Theory Illustrations for Non-Smooth, Nonlinear Data
40 2.10 Matrix Algebra, Notation 44 2.11 Equation Solving, Linear Algebra
46 2.12 Krylov Sparse Matrix Solver Methodology 53 2.13 Summary 54
Exercises 54 References 56 3 Aerodynamics I: Potential flow, GWSh theory
exposition, transonic flow mPDE shock capturing 59 3.1 Aerodynamics, Weak
Interaction 59 3.2 Navier-Stokes Manipulations for Aerodynamics 60 3.3
Steady Potential Flow GWS 62 3.4 Accuracy, Convergence, Mathematical
Preliminaries 66 3.5 Accuracy, Galerkin Weak Form Optimality 68 3.6
Accuracy, GWSh Error Bound 71 3.7 Accuracy, GWSh Asymptotic Convergence 73
3.8 GWSh Natural Coordinate FE Basis Matrices 76 3.9 GWSh Tensor Product FE
Basis Matrices 82 3.10 GWSh Comparison with Laplacian FD and FV Stencils 87
3.11 Post-Processing Pressure Distributions 90 3.12 Transonic Potential
Flow, Shock Capturing 92 3.13 Summary 96 Exercises 98 References 99 4
Aerodynamics II: boundary layers, turbulence closure modeling, parabolic
Navier-Stokes 101 4.1 Aerodynamics, Weak Interaction Reprise 101 4.2
Navier-Stokes PDE System Reynolds Ordered 102 4.3 GWSh, n= 2
Laminar-Thermal Boundary Layer 104 4.4 GWSh + thetaTS BL Matrix Iteration
Algorithm 108 4.5 Accuracy, Convergence, Optimal Mesh Solutions 111 4.6
GWSh +thetaTS Solution Optimality, Data Influence 115 4.7 Time Averaged NS,
Turbulent BL Formulation 116 4.8 Turbulent BL GWSh+ thetaTS, Accuracy,
Convergence 120 4.9 GWSh+ thetaTS BL Algorithm, TKE Closure Models 123 4.10
The Parabolic Navier-Stokes PDE System 129 4.11 GWSh +thetaTS Algorithm for
PNS PDE System 134 4.12 GWSh +thetaTS k=1 NC Basis PNS Algorithm 137 4.13
Weak Interaction PNS Algorithm Validation 141 4.14 Square Duct PNS
Algorithm Validation 147 4.15 Summary 148 Exercises 155 References 157 5
The Navier-Stokes Equations: theoretical fundamentals; constraint, spectral
analyses, mPDE theory, optimal Galerkin weak forms 159 5.1 The
Incompressible Navier-Stokes PDE System 159 5.2 Continuity Constraint,
Exact Enforcement 160 5.3 Continuity Constraint, Inexact Enforcement 164
5.4 The CCM Pressure Projection Algorithm 166 5.5 Convective Transport,
Phase Velocity 168 5.6 Convection-Diffusion, Phase Speed Characterization
170 5.7 Theory for Optimal mGWSh+ thetaTS Phase Accuracy 177 5.8 Optimally
Phase Accurate mGWSh + thetaTS in n Dimensions 185 5.9 Theory for Optimal
mGWSh Asymptotic Convergence 193 5.10 The Optimal mGWSh ? thetaTS k ? 1
Basis NS Algorithm 201 5.11 Summary 203 Exercises 206 References 208 6
Vector Field Theory Implementations: vorticity-streamfunction,
vorticity-velocity formulations 211 6.1 Vector Field Theory NS PDE
Manipulations 211 6.2 Vorticity-Streamfunction PDE System, n= 2 213 6.3
Vorticity-Streamfunction mGWSh Algorithm 214 6.4 Weak Form Theory
Verification, GWSh/mGWSh 219 6.5 Vorticity-Velocity mGWSh Algorithm, n= 3
228 6.6 Vorticity-Velocity GWSh+ thetaTS Assessments, n= 3 233 6.7 Summary
243 Exercises 246 References 247 7 Classic State Variable Formulations:
GWS/mGWSh+thetaTS algorithms for Navier-Stokes; accuracy, convergence,
validation, BCs, radiation, ALE formulation 249 7.1 Classic State Variable
Navier-Stokes PDE System 249 7.2 NS Classic State Variable mPDE System 251
7.3 NS Classic State Variable mGWSh+ thetaTS Algorithm 252 7.4 NS mGWSh
+thetaTS Algorithm Discrete Formation 254 7.5 mGWSh+ thetaTS Algorithm
Completion 258 7.6 mGWSh+ thetaTS Algorithm Benchmarks, n=2 260 7.7 mGWSh+
thetaTS Algorithm Validations, n= 3 268 7.8 Flow Bifurcation, Multiple
Outflow Pressure BCs 282 7.9 Convection/Radiation BCs in GWSh+ thetaTS 283
7.10 Convection BCs Validation 288 7.11 Radiosity, GWSh Algorithm 295 7.12
Radiosity BC, Accuracy, Convergence, Validation 298 7.13 ALE
Thermo-Solid-Fluid-Mass Transport Algorithm 302 7.14 ALE GWSh +thetaTS
Algorithm LISI Validation 304 7.15 Summary 310 Exercises 317 References 318
8 Time Averaged Navier-Stokes: mGWSh+thetaTS algorithm for RaNS, Reynolds
stress tensor closure models 319 8.1 Classic State Variable RaNS PDE System
319 8.2 RaNS PDE System Turbulence Closure 321 8.3 RaNS State Variable mPDE
System 323 8.4 RaNS mGWSh+thetaTS Algorithm Matrix Statement 325 8.5 RaNS
mGWSh + thetaTS Algorithm, Stability, Accuracy 331 8.6 RaNS Algorithm BCs
for Conjugate Heat Transfer 337 8.7 RaNS Full Reynolds Stress Closure PDE
System 341 8.8 RSM Closure mGWSh +thetaTS Algorithm 345 8.9 RSM Closure
Model Validation 347 8.10 Geologic Borehole Conjugate Heat Transfer 348
8.11 Summary 358 Exercises 363 References 364 9 Space Filtered
Navier-Stokes: GWSh/mGWSh+thetaTS for space filtered Navier-Stokes,
modeled, analytical closure 365 9.1 Classic State Variable LES PDE System
365 9.2 Space Filtered NS PDE System 366 9.3 SGS Tensor Closure Modeling
for LES 368 9.4 Rational LES Theory Predictions 371 9.5 RLES Unresolved
Scale SFS Tensor Models 376 9.6 Analytical SFS Tensor/Vector Closures 381
9.7 Auxiliary Problem Resolution Via Perturbation Theory 383 9.8 LES
Analytical Closure (arLES) Theory 386 9.9 arLES Theory mGWSh + thetaTS
Algorithm 387 9.10 arLES Theory mGWSh + thetaTS Completion 391 9.11 arLES
Theory Implementation Diagnostics 392 9.12 RLES Theory Turbulent BL
Validation 403 9.13 Space Filtered NS PDE System on Bounded Domains 409
9.14 Space Filtered NS Bounded Domain BCs 410 9.15 ADBC Algorithm
Validation, Space Filtered DE 412 9.16 arLES Theory Resolved Scale BCE
Integrals 420 9.17 Turbulent Resolved Scale Velocity BC Optimal
Omegah-delta 423 9.18 Resolved Scale Velocity DBC Validation 8 Re 430 9.19
arLES O(delta2) State Variable Bounded Domain BCs 430 9.20 Well-Posed arLES
Theory n = 3 Validation 433 9.21 Well-Posed arLES Theory n = 3 Diagnostics
441 9.22 Summary 446 Exercises 455 References 456 10 Summary-VVUQ:
verification, validation, uncertainty quantification 459 10.1 Beyond
Colorful Fluid Dynamics 459 10.2 Observations on Computational Reliability
460 10.3 Solving the Equations Right 461 10.4 Solving the Right Equations
464 10.5 Solving the Right Equations Without Modeling 466 10.6 Solving the
Right Equations Well-Posed 468 10.7 Well-Posed Right Equations Optimal CFD
471 10.8 The Right Closing Caveat 473 References 474 Appendix A: Well-Posed
arLES Theory PICMSS Template 475 Appendix B: Hypersonic Parabolic
Navier-Stokes 483 B.1 High Speed External Aerodynamics 483 B.2 Compressible
Navier-Stokes PDE System 484 B.3 Parabolic Compressible RaNS PDE System 488
B.4 Compressible PRaNS mPDE System Closure 490 B.5 Bow Shock Fitting, PRaNS
State Variable IC 493 B.6 The PRaNS mGWSh+thetaTS Algorithm 496 B.7 PRaNS
mGWSh+thetaTS Algorithm Completion 501 B.8 PRaNS Algorithm IC Generation
505 B.9 PRaNS mGWSh+thetaTS Algorithm Validation 507 B.10 Hypersonic Blunt
Body Shock Trajectory 515 B.11 Shock Trajectory Characteristics Algorithm
521 B.12 Blunt Body PRaNS Algorithm Validation 523 B.13 Summary 527
Exercises 532 References 533 Author Index 535 Subject Index 541