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Optimal Modified Continuous Galerkin CFD.

By: Publisher: New York : John Wiley & Sons, Incorporated, 2014Copyright date: ©2013Edition: 1st edDescription: 1 online resource (654 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781118403075
Subject(s): Genre/Form: Additional physical formats: Print version:: Optimal Modified Continuous Galerkin CFDDDC classification:
  • 518/.63
LOC classification:
  • TA357 -- .B354 2014eb
Online resources:
Contents:
Intro -- Title Page -- Copyright -- Dedication -- Preface -- About the Author -- Notations -- Chapter 1: Introduction -- 1.1 About This Book -- 1.2 The Navier-Stokes Conservation Principles System -- 1.3 Navier-Stokes PDE System Manipulations -- 1.4 Weak Form Overview -- 1.5 A Brief History of Finite Element CFD -- 1.6 A Brief Summary -- References -- Chapter 2: Concepts, Terminology, Methodology -- 2.1 Overview -- 2.2 Steady DE Weak Form Completion -- 2.3 Steady DE GWSN Discrete FE Implementation -- 2.4 PDE Solutions, Classical Concepts -- 2.5 The Sturm-Liouville Equation, Orthogonality, Completeness -- 2.6 Classical Variational Calculus -- 2.7 Variational Calculus, Weak Form Duality -- 2.8 Quadratic Forms, Norms, Error Estimation -- 2.9 Theory Illustrations for Non-Smooth, Nonlinear Data -- 2.10 Matrix Algebra, Notation -- 2.11 Equation Solving, Linear Algebra -- 2.12 Krylov Sparse Matrix Solver Methodology -- 2.13 Summary -- Exercises -- References -- Chapter 3: Aerodynamics I: -- 3.1 Aerodynamics, Weak Interaction -- 3.2 Navier-Stokes Manipulations for Aerodynamics -- 3.3 Steady Potential Flow GWS -- 3.4 Accuracy, Convergence, Mathematical Preliminaries -- 3.5 Accuracy, Galerkin Weak Form Optimality -- 3.6 Accuracy, GWSh Error Bound -- 3.7 Accuracy, GWSh Asymptotic Convergence -- 3.8 GWSh Natural Coordinate FE Basis Matrices -- 3.9 GWSh Tensor Product FE Basis Matrices -- 3.10 GWSh Comparison with Laplacian FD and FV Stencils -- 3.11 Post-Processing Pressure Distributions -- 3.12 Transonic Potential Flow, Shock Capturing -- 3.13 Summary -- Exercises -- References -- Chapter 4: Aerodynamics II: -- 4.1 Aerodynamics, Weak Interaction Reprise -- 4.2 Navier-Stokes PDE System Reynolds Ordered -- 4.3 GWSh, n = 2 Laminar-Thermal Boundary Layer -- 4.4 GWSh + θTS BL Matrix Iteration Algorithm -- 4.5 Accuracy, Convergence, Optimal Mesh Solutions.
4.6 GWSh + θTS Solution Optimality, Data Influence -- 4.7 Time Averaged NS, Turbulent BL Formulation -- 4.8 Turbulent BL GWSh + θTS, Accuracy, Convergence -- 4.9 GWSh+ θTS BL Algorithm, TKE Closure Models -- 4.10 The Parabolic Navier-Stokes PDE System -- 4.11 GWSh + θTS Algorithm for PNS PDE System -- 4.12 GWSh + θTS k = 1 NC Basis PNS Algorithm -- 4.13 Weak Interaction PNS Algorithm Validation -- 4.14 Square Duct PNS Algorithm Validation -- 4.15 Summary -- Exercises -- References -- Chapter 5: The Navier-Stokes Equations: -- 5.1 The Incompressible Navier-Stokes PDE System -- 5.2 Continuity Constraint, Exact Enforcement -- 5.3 Continuity Constraint, Inexact Enforcement -- 5.4 The CCM Pressure Projection Algorithm -- 5.5 Convective Transport, Phase Velocity -- 5.6 Convection-Diffusion, Phase Speed Characterization -- 5.7 Theory for Optimal mGWSh + θTS Phase Accuracy -- 5.8 Optimally Phase Accurate mGWSh + θTS in n Dimensions -- 5.9 Theory for Optimal mGWSh Asymptotic Convergence -- 5.10 The Optimal mGWSh + θTS k = 1 Basis NS Algorithm -- 5.11 Summary -- Exercises -- References -- Chapter 6: Vector Field Theory Implementations: -- 6.1 Vector Field Theory NS PDE Manipulations -- 6.2 Vorticity-Streamfunction PDE System, n = 2 -- 6.3 Vorticity-Streamfunction mGWShAlgorithm -- 6.4 Weak Form Theory Verification, GWSh/mGWSh -- 6.5 Vorticity-Velocity mGWShAlgorithm, n = 3 -- 6.6 Vorticity-Velocity GWSh + θTS Assessments, n = 3 -- 6.7 Summary -- Exercises -- References -- Chapter 7: Classic State Variable Formulations: -- 7.1 Classic State Variable Navier-Stokes PDE System -- 7.2 NS Classic State Variable mPDE System -- 7.3 NS Classic State Variable mGWSh + θTS Algorithm -- 7.4 NS mGWSh + θTS Algorithm Discrete Formation -- 7.5 mGWSh + θTS Algorithm Completion -- 7.6 mGWSh+θTS Algorithm Benchmarks, n = 2 -- 7.7 mGWSh + θTS Algorithm Validations, n = 3.
7.8 Flow Bifurcation, Multiple Outflow Pressure BCs -- 7.9 Convection/Radiation BCs in GWSh + θTS -- 7.10 Convection BCs Validation -- 7.11 Radiosity, GWSh Algorithm -- 7.12 Radiosity BC, Accuracy, Convergence, Validation -- 7.13 ALE Thermo-Solid-Fluid-Mass Transport Algorithm -- 7.14 ALE GWSh + θTS Algorithm LISI Validation -- 7.15 Summary -- Exercises -- References -- Chapter 8: Time Averaged Navier-Stokes: -- 8.1 Classic State Variable RaNS PDE System -- 8.2 RaNS PDE System Turbulence Closure -- 8.3 RaNS State Variable mPDE System -- 8.4 RaNS mGWSh + θTS Algorithm Matrix Statement -- 8.5 RaNS mGWSh + θTS Algorithm, Stability, Accuracy -- 8.6 RaNS Algorithm BCs for Conjugate Heat Transfer -- 8.7 RaNS Full Reynolds Stress Closure PDE System -- 8.8 RSM Closure mGWSh + θTS Algorithm -- 8.9 RSM Closure Model Validation -- 8.10 Geologic Borehole Conjugate Heat Transfer -- 8.11 Summary -- Exercises -- References -- Chapter 9: Space Filtered Navier-Stokes: -- 9.1 Classic State Variable LES PDE System -- 9.2 Space Filtered NS PDE System -- 9.3 SGS Tensor Closure Modeling for LES -- 9.4 Rational LES Theory Predictions -- 9.5 RLES Unresolved Scale SFS Tensor Models -- 9.6 Analytical SFS Tensor/Vector Closures -- 9.7 Auxiliary Problem Resolution Via Perturbation Theory -- 9.8 LES Analytical Closure (arLES) Theory -- 9.9 arLES Theory mGWSh + θTS Algorithm -- 9.10 arLES Theory mGWSh + θTS Completion -- 9.11 arLES Theory Implementation Diagnostics -- 9.12 RLES Theory Turbulent BL Validation -- 9.13 Space Filtered NS PDE System on Bounded Domains -- 9.14 Space Filtered NS Bounded Domain BCs -- 9.15 ADBC Algorithm Validation, Space Filtered DE -- 9.16 arLES Theory Resolved Scale BCE Integrals -- 9.17 Turbulent Resolved Scale Velocity BC Optimal Ωh-δ -- 9.18 Resolved Scale Velocity DBC Validation ∀ Re -- 9.19 arLES O(δ2) State Variable Bounded Domain BCs.
9.20 Well-Posed arLES Theory n = 3 Validation -- 9.21 Well-Posed arLES Theory n = 3 Diagnostics -- 9.22 Summary -- Exercises -- References -- Chapter 10: Summary - VVUQ: -- 10.1 Beyond Colorful Fluid Dynamics -- 10.2 Observations on Computational Reliability -- 10.3 Solving the Equations Right -- 10.4 Solving the Right Equations -- 10.5 Solving the Right Equations Without Modeling -- 10.6 Solving the Right Equations Well-Posed -- 10.7 Well-Posed Right Equations Optimal CFD -- 10.8 The Right Closing Caveat -- References -- Appendix A Well-Posed arLES Theory PICMSS Template -- Appendix B Hypersonic Parabolic Navier-Stokes:Parabolic Time Averaged Compressible NS for Hypersonic Shock Layer Aerothermodynamics -- Author Index -- Subject Index -- End User License Agreement.
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.
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Intro -- Title Page -- Copyright -- Dedication -- Preface -- About the Author -- Notations -- Chapter 1: Introduction -- 1.1 About This Book -- 1.2 The Navier-Stokes Conservation Principles System -- 1.3 Navier-Stokes PDE System Manipulations -- 1.4 Weak Form Overview -- 1.5 A Brief History of Finite Element CFD -- 1.6 A Brief Summary -- References -- Chapter 2: Concepts, Terminology, Methodology -- 2.1 Overview -- 2.2 Steady DE Weak Form Completion -- 2.3 Steady DE GWSN Discrete FE Implementation -- 2.4 PDE Solutions, Classical Concepts -- 2.5 The Sturm-Liouville Equation, Orthogonality, Completeness -- 2.6 Classical Variational Calculus -- 2.7 Variational Calculus, Weak Form Duality -- 2.8 Quadratic Forms, Norms, Error Estimation -- 2.9 Theory Illustrations for Non-Smooth, Nonlinear Data -- 2.10 Matrix Algebra, Notation -- 2.11 Equation Solving, Linear Algebra -- 2.12 Krylov Sparse Matrix Solver Methodology -- 2.13 Summary -- Exercises -- References -- Chapter 3: Aerodynamics I: -- 3.1 Aerodynamics, Weak Interaction -- 3.2 Navier-Stokes Manipulations for Aerodynamics -- 3.3 Steady Potential Flow GWS -- 3.4 Accuracy, Convergence, Mathematical Preliminaries -- 3.5 Accuracy, Galerkin Weak Form Optimality -- 3.6 Accuracy, GWSh Error Bound -- 3.7 Accuracy, GWSh Asymptotic Convergence -- 3.8 GWSh Natural Coordinate FE Basis Matrices -- 3.9 GWSh Tensor Product FE Basis Matrices -- 3.10 GWSh Comparison with Laplacian FD and FV Stencils -- 3.11 Post-Processing Pressure Distributions -- 3.12 Transonic Potential Flow, Shock Capturing -- 3.13 Summary -- Exercises -- References -- Chapter 4: Aerodynamics II: -- 4.1 Aerodynamics, Weak Interaction Reprise -- 4.2 Navier-Stokes PDE System Reynolds Ordered -- 4.3 GWSh, n = 2 Laminar-Thermal Boundary Layer -- 4.4 GWSh + θTS BL Matrix Iteration Algorithm -- 4.5 Accuracy, Convergence, Optimal Mesh Solutions.

4.6 GWSh + θTS Solution Optimality, Data Influence -- 4.7 Time Averaged NS, Turbulent BL Formulation -- 4.8 Turbulent BL GWSh + θTS, Accuracy, Convergence -- 4.9 GWSh+ θTS BL Algorithm, TKE Closure Models -- 4.10 The Parabolic Navier-Stokes PDE System -- 4.11 GWSh + θTS Algorithm for PNS PDE System -- 4.12 GWSh + θTS k = 1 NC Basis PNS Algorithm -- 4.13 Weak Interaction PNS Algorithm Validation -- 4.14 Square Duct PNS Algorithm Validation -- 4.15 Summary -- Exercises -- References -- Chapter 5: The Navier-Stokes Equations: -- 5.1 The Incompressible Navier-Stokes PDE System -- 5.2 Continuity Constraint, Exact Enforcement -- 5.3 Continuity Constraint, Inexact Enforcement -- 5.4 The CCM Pressure Projection Algorithm -- 5.5 Convective Transport, Phase Velocity -- 5.6 Convection-Diffusion, Phase Speed Characterization -- 5.7 Theory for Optimal mGWSh + θTS Phase Accuracy -- 5.8 Optimally Phase Accurate mGWSh + θTS in n Dimensions -- 5.9 Theory for Optimal mGWSh Asymptotic Convergence -- 5.10 The Optimal mGWSh + θTS k = 1 Basis NS Algorithm -- 5.11 Summary -- Exercises -- References -- Chapter 6: Vector Field Theory Implementations: -- 6.1 Vector Field Theory NS PDE Manipulations -- 6.2 Vorticity-Streamfunction PDE System, n = 2 -- 6.3 Vorticity-Streamfunction mGWShAlgorithm -- 6.4 Weak Form Theory Verification, GWSh/mGWSh -- 6.5 Vorticity-Velocity mGWShAlgorithm, n = 3 -- 6.6 Vorticity-Velocity GWSh + θTS Assessments, n = 3 -- 6.7 Summary -- Exercises -- References -- Chapter 7: Classic State Variable Formulations: -- 7.1 Classic State Variable Navier-Stokes PDE System -- 7.2 NS Classic State Variable mPDE System -- 7.3 NS Classic State Variable mGWSh + θTS Algorithm -- 7.4 NS mGWSh + θTS Algorithm Discrete Formation -- 7.5 mGWSh + θTS Algorithm Completion -- 7.6 mGWSh+θTS Algorithm Benchmarks, n = 2 -- 7.7 mGWSh + θTS Algorithm Validations, n = 3.

7.8 Flow Bifurcation, Multiple Outflow Pressure BCs -- 7.9 Convection/Radiation BCs in GWSh + θTS -- 7.10 Convection BCs Validation -- 7.11 Radiosity, GWSh Algorithm -- 7.12 Radiosity BC, Accuracy, Convergence, Validation -- 7.13 ALE Thermo-Solid-Fluid-Mass Transport Algorithm -- 7.14 ALE GWSh + θTS Algorithm LISI Validation -- 7.15 Summary -- Exercises -- References -- Chapter 8: Time Averaged Navier-Stokes: -- 8.1 Classic State Variable RaNS PDE System -- 8.2 RaNS PDE System Turbulence Closure -- 8.3 RaNS State Variable mPDE System -- 8.4 RaNS mGWSh + θTS Algorithm Matrix Statement -- 8.5 RaNS mGWSh + θTS Algorithm, Stability, Accuracy -- 8.6 RaNS Algorithm BCs for Conjugate Heat Transfer -- 8.7 RaNS Full Reynolds Stress Closure PDE System -- 8.8 RSM Closure mGWSh + θTS Algorithm -- 8.9 RSM Closure Model Validation -- 8.10 Geologic Borehole Conjugate Heat Transfer -- 8.11 Summary -- Exercises -- References -- Chapter 9: Space Filtered Navier-Stokes: -- 9.1 Classic State Variable LES PDE System -- 9.2 Space Filtered NS PDE System -- 9.3 SGS Tensor Closure Modeling for LES -- 9.4 Rational LES Theory Predictions -- 9.5 RLES Unresolved Scale SFS Tensor Models -- 9.6 Analytical SFS Tensor/Vector Closures -- 9.7 Auxiliary Problem Resolution Via Perturbation Theory -- 9.8 LES Analytical Closure (arLES) Theory -- 9.9 arLES Theory mGWSh + θTS Algorithm -- 9.10 arLES Theory mGWSh + θTS Completion -- 9.11 arLES Theory Implementation Diagnostics -- 9.12 RLES Theory Turbulent BL Validation -- 9.13 Space Filtered NS PDE System on Bounded Domains -- 9.14 Space Filtered NS Bounded Domain BCs -- 9.15 ADBC Algorithm Validation, Space Filtered DE -- 9.16 arLES Theory Resolved Scale BCE Integrals -- 9.17 Turbulent Resolved Scale Velocity BC Optimal Ωh-δ -- 9.18 Resolved Scale Velocity DBC Validation ∀ Re -- 9.19 arLES O(δ2) State Variable Bounded Domain BCs.

9.20 Well-Posed arLES Theory n = 3 Validation -- 9.21 Well-Posed arLES Theory n = 3 Diagnostics -- 9.22 Summary -- Exercises -- References -- Chapter 10: Summary - VVUQ: -- 10.1 Beyond Colorful Fluid Dynamics -- 10.2 Observations on Computational Reliability -- 10.3 Solving the Equations Right -- 10.4 Solving the Right Equations -- 10.5 Solving the Right Equations Without Modeling -- 10.6 Solving the Right Equations Well-Posed -- 10.7 Well-Posed Right Equations Optimal CFD -- 10.8 The Right Closing Caveat -- References -- Appendix A Well-Posed arLES Theory PICMSS Template -- Appendix B Hypersonic Parabolic Navier-Stokes:Parabolic Time Averaged Compressible NS for Hypersonic Shock Layer Aerothermodynamics -- Author Index -- Subject Index -- End User License Agreement.

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.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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