Optimal modified continuous Galerkin CFD / A. J. Baker.

Format:

Book

Author/Creator:

Baker, A. J., 1936- author.

Language:

English

Subjects (All):

Fluid mechanics.

Finite element method.

Galerkin methods.

Physical Description:

1 online resource (576 p.)

Edition:

1st ed.

Place of Publication:

Chichester, England : Wiley, 2014.

Language Note:

English

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"-- Provided by publisher.

"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.

Contents:

Optimal Modified Continuous Galerkin CFD; Contents; Preface; About the Author; Notations; 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; 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; 3 Aerodynamics I: Potential flow, GWSh theory exposition, transonic flow mPDE shock capturing; 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; 4 Aerodynamics II: boundary layers, turbulence closure modeling, parabolic Navier-Stokes; 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 5 The Navier-Stokes Equations: theoretical fundamentals; constraint, spectral analyses, mPDE theory, optimal Galerkin weak forms; 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

Notes:

Description based upon print version of record.

Includes bibliographical references at the end of each chapters and index.

Description based on print version record.

ISBN:

9781118402719

1118402715

9781118403075

111840307X

9781118403082

1118403088

OCLC:

870530870