Optimal modified continuous Galerkin CFD

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Title:

Personal Author:

Baker, A. J., 1936-, author

Publication Information:

Chichester, West Sussex, United Kingdom : John Wiley & Sons Inc., 2014

Physical Description:

xxiv, 550 pages : illustrations ; 24 cm.

ISBN:

9781119940494

Abstract:

"This book promotes the use of optimal modified continuous Galerkin weak form theory to generate discrete approximate solutions to incompressible-thermal Navier-Stokes equations"--provided by publisher

Subject Term:

Fluid mechanics

Finite element method

Galerkin methods

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010336651	TA357 B354 2014	Open Access Book	Book	Searching... Unknown

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Summary

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.

Author Notes

A.J. Baker is Professor Emeritus, Engineering Science and Mechanics, The University of Tennessee, USA. He is an elected Fellow of the International Association for Computational Mechanics (IACM) and the US Association for Computational Mechanics (USACM) and an Associate Fellow of the American Institute of Aeronautics and Astronautics (AIAA).

Preface	p. xiii
About the Author	p. xvii
Notations	p. xix
1 Introduction	p. 1
1.1 About This Book	p. 1
1.2 The Navier-Stokes Conservation Principles System	p. 2
1.3 Navier-Stokes PDE System Manipulations	p. 5
1.4 Weak Form Overview	p. 7
1.5 A Brief History of Finite Element CFD	p. 9
1.6 A Brief Summary	p. 11
References	p. 12
2 Concepts, terminology, methodology	p. 15
2.1 Overview	p. 15
2.2 Steady DE Weak Form Completion	p. 16
2.3 Steady DE GWS N Discrete FE Implementation	p. 19
2.4 PDE Solutions, Classical Concepts	p. 27
2.5 The Sturm-Liouville Equation, Orthogonality, Completeness	p. 30
2.6 Classical Variational Calculus	p. 33
2.7 Variational Calculus, Weak Form Duality	p. 36
2.8 Quadratic Forms, Norms, Error Estimation	p. 38
2.9 Theory Illustrations for Non-Smooth, Nonlinear Data	p. 40
2.10 Matrix Algebra, Notation	p. 44
2.11 Equation Solving, Linear Algebra	p. 46
2.12 Krylov Sparse Matrix Solver Methodology	p. 53
2.13 Summary	p. 54
Exercises	p. 54
References	p. 56
3 Aerodynamics I: Potential flow, GWS h theory exposition, transonic flow mPDE shock capturing	p. 59
3.1 Aerodynamics, Weak Interaction	p. 59
3.2 Navier-Stokes Manipulations for Aerodynamics	p. 60
3.3 Steady Potential Flow GWS	p. 62
3.4 Accuracy, Convergence, Mathematical Preliminaries	p. 66
3.5 Accuracy, Galerkin Weak Form Optimality	p. 68
3.6 Accuracy, GWS h Error Bound	p. 71
3.7 Accuracy, GWS h Asymptotic Convergence	p. 73
3.8 GWS h Natural Coordinate FE Basis Matrices	p. 76
3.9 GWS h Tensor Product FE Basis Matrices	p. 82
3.10 GWS h Comparison with Laplacian FD and FV Stencils	p. 87
3.11 Post-Processing Pressure Distributions	p. 90
3.12 Transonic Potential Flow, Shock Capturing	p. 92
3.13 Summary	p. 96
Exercises	p. 98
References	p. 99
4 Aerodynamics II: boundary layers, turbulence closure modeling, parabolic Navier-Stokes	p. 101
4.1 Aerodynamics, Weak Interaction Reprise	p. 101
4.2 Navier-Stokes PDE System Reynolds Ordered	p. 102
4.3 GWS h , n = 2 Laminar-Thermal Boundary Layer	p. 104
4.4 GWS h + ¿TS BL Matrix Iteration Algorithm	p. 108
4.5 Accuracy, Convergence, Optimal Mesh Solutions	p. 111
4.6 GWS h + ¿TS Solution Optimality, Data Influence	p. 115
4.7 Time Averaged NS, Turbulent BL Formulation	p. 116
4.8 Turbulent BL GWS h + ¿TS, Accuracy, Convergence	p. 120
4.9 GWS h +¿TS BL Algorithm, TKE Closure Models	p. 123
4.10 The Parabolic Navier-Stokes PDE System	p. 129
4.11 GWS h + ¿TS Algorithm for PNS PDE System	p. 134
4.12 GWS h + ¿TS k=1 NC Basis PNS Algorithm	p. 137
4.13 Weak Interaction PNS Algorithm Validation	p. 141
4.14 Square Duct PNS Algorithm Validation	p. 147
4.15 Summary	p. 148
Exercises	p. 155
References	p. 157
5 The Navier-Stokes Equations: theoretical fundamentals; constraint, spectral analyses, mPDE theory, optimal Galerkin weak forms	p. 159
5.1 The Incompressible Navier-Stokes PDE System	p. 159
5.2 Continuity Constraint, Exact Enforcement	p. 160
5.3 Continuity Constraint, Inexact Enforcement	p. 164
5.4 The CCM Pressure Projection Algorithm	p. 166
5.5 Convective Transport, Phase Velocity	p. 168
5.6 Convection-Diffusion, Phase Speed Characterization	p. 170
5.7 Theory for Optimal mGWS h + ¿TS Phase Accuracy	p. 177
5.8 Optimally Phase Accurate mGWS h + ¿TS in n Dimensions	p. 185
5.9 Theory for Optimal mGWS h Asymptotic Convergence	p. 193
5.10 The Optimal mGWS h + ¿TS k = 1 Basis NS Algorithm	p. 201
5.11 Summary	p. 203
Exercises	p. 206
References	p. 208
6 Vector Field Theory Implementations: vorticity-streamfunction, vorticity-velocity formulations	p. 211
6.1 Vector Field Theory NS PDE Manipulations	p. 211
6.2 Vorticity-Streamfunction PDE System, n = 2	p. 213
6.3 Vorticity-Streamfunction mGWS h Algorithm	p. 214
6.4 Weak Form Theory Verification, GWS h /mGWS h	p. 219
6.5 Vorticity-Velocity mGWS h Algorithm, n = 3	p. 228
6.6 Vorticity-Velocity GWS h + ¿TS Assessments, n = 3	p. 233
6.7 Summary	p. 243
Exercises	p. 246
References	p. 247
7 Classic State Variable Formulations: GWS/mGWS h + ¿TS algorithms for Navier-Stokes; accuracy, convergence, validation, BCs, radiation, ALE formulation	p. 249
7.1 Classic Slate Variable Navier-Stokes PDE System	p. 249
7.2 NS Classic State Variable mPDE System	p. 251
7.3 NS Classic State Variable mGWS h + ¿TS Algorithm	p. 252
7.4 NS mGWS h + ¿TS Algorithm Discrete Formation	p. 254
7.5 mGWS h + ¿TS Algorithm Completion	p. 258
7.6 mGWS h + ¿TS Algorithm Benchmarks, n = 2	p. 260
7.7 mGWS h + ¿TS Algorithm Validations, n = 3	p. 268
7.8 Flow Bifurcation, Multiple Outflow Pressure BCs	p. 282
7.9 Convection/Radiation BCs in GWS h + ¿TS	p. 283
7.10 Convection BCs Validation	p. 288
7.11 Radiosity, GWS h Algorithm	p. 295
7.12 Radiosity BC, Accuracy, Convergence, Validation	p. 298
7.13 ALE Thermo-Solid-Fluid-Mass Transport Algorithm	p. 302
7.14 ALE GWS h + ¿TS Algorithm LISI Validation	p. 304
7.15 Summary	p. 310
Exercises	p. 317
References	p. 318
8 Time Averaged Navier-Stokes: mGWS h + ¿TS algorithm for RaNS, Reynolds stress tensor closure models	p. 319
8.1 Classic State Variable RaNS PDE System	p. 319
8.2 RaNS PDE System Turbulence Closure	p. 321
8.3 RaNS State Variable mPDE System	p. 323
8.4 RaNS mGWS h + ¿TS Algorithm Matrix Statement	p. 325
8.5 RaNS mGWS h + ¿TS Algorithm, Stability, Accuracy	p. 331
8.6 RaNS Algorithm BCs for Conjugate Heat Transfer	p. 337
8.7 RaNS Full Reynolds Stress Closure PDE System	p. 341
8.8 RSM Closure mGWS h + ¿TS Algorithm	p. 345
8.9 RSM Closure Model Validation	p. 347
8.10 Geologic Borehole Conjugate Heal Transfer	p. 348
8.11 Summary	p. 358
Exercises	p. 363
References	p. 364
9 Space Filtered Navier-Stokes: GWS h /GWS h + ¿TS for space filtered Navier-Stokes, modeled, analytical closure	p. 365
9.1 Classic State Variable LES PDE System	p. 365
9.2 Space Filtered NS PDE System	p. 366
9.3 SGS Tensor Closure Modeling for LES	p. 368
9.4 Rational LES Theory Predictions	p. 371
9.5 RLES Unresolved Scale SFS Tensor Models	p. 376
9.6 Analytical SFS Tensor/Vector Closures	p. 381
9.7 Auxiliary Problem Resolution Via Perturbation Theory	p. 383
9.8 LES Analytical Closure (arLES) Theory	p. 386
9.9 arLES Theory mGWS h + ¿TS Algorithm	p. 387
9.10 arLES Theory mGWS h + ¿TS Completion	p. 391
9.11 arLES Theory Implementation Diagnostics	p. 392
9.12 RLES Theory Turbulent BL Validation	p. 403
9.13 Space Filtered NS PDE System on Bounded Domains	p. 409
9.14 Space Filtered NS Bounded Domain BCs	p. 410
9.15 ADBC Algorithm Validation, Space Filtered DE	p. 412
9.16 arLES Theory Resolved Scale BCE integrals	p. 420
9.17 Turbulent Resolved Scale Velocity BC Optimal ¿ h -¿	p. 423
9.18 Resolved Scale Velocity DBC Validation ∀ Re	p. 430
9.19 arLES O(¿ 2 ) State Variable Bounded Domain BCs	p. 430
9.20 Well-Posed arLES Theory n = 3 Validation	p. 433
9.21 Well-Posed arLES Theory n = 3 Diagnostics	p. 441
9.22 Summary	p. 446
Exercises	p. 455
References	p. 456
10 Summary-VVUQ: verification, validation, uncertainty quantification	p. 459
10.1 Beyond Colorful Fluid Dynamics	p. 459
10.2 Observations on Computational Reliability	p. 460
10.3 Solving the Equations Right	p. 461
10.4 Solving the Right Equations	p. 464
10.5 Solving the Right Equations Without Modeling	p. 466
10.6 Solving the Right Equations Well-Posed	p. 468
10.7 Well-Posed Right Equations Optimal CFD	p. 471
10.8 The Right Closing Caveat	p. 473
References	p. 474
Appendix A Well-Posed arLES Theory PICMSS Template	p. 475
Appendix B Hypersonic Parabolic Navier-Stokes	p. 483
B.1 High Speed External Aerodynamics	p. 483
B.2 Compressible Navier-Stokes PDE System	p. 484
B.3 Purabolic Compressible RaNS PDE System	p. 488
B.4 Compressible PRaNS mPDE System Closure	p. 490
B.5 Bow Shock Fitting, PRaNS State Variable IC	p. 493
B.6 The PRaNS mGWS h + ¿TS Algorithm	p. 496
B.7 PRaNS mGWS h -¿TS Algorithm Completion	p. 501
B.8 PRaNS Algorithm IC Generation	p. 505
B.9 PRaNS mGWS h + ¿TS Algorithm Validation	p. 507
B.10 Hypersonic Blunt Body Shock Trajectory	p. 515
B.11 Shock Trajectory Characteristics Algorithm	p. 521
B.12 Blunt Body PRaNS Algorithm Validation	p. 523
B.13 Summary	p. 527
Exercises	p. 532
References	p. 533
Author Index	p. 535
Subject Index	p. 541

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Table of Contents