Incompressible Flow and the Finite Element Method, Volume 2, Isothermal Laminar FlowISBN: 9780471492504
632 pages
June 2000

This comprehensive twovolume reference covers the application of the finite element method to incompressible flows in fluid mechanics, addressing the theoretical background and the development of appropriate numerical methods applied to their solution.
Volume One provides extensive coverage of the prototypical fluid mechanics equation: the advectiondiffusion equation. For both this equation and the equations of principal interest  the NavierStokes equations (covered in detail in Volume Two)  a discussion of both the continuous and discrete equations is presented, as well as explanations of how to properly march the timedependent equations using smart implicit methods. Boundary and initial conditions, so important in applications, are carefully described and discussed, including wellposedness. The important role played by the pressure, so confusing in the past, is carefully explained.
The book explains and emphasizes consistency in six areas:
* consistent mass matrix
* consistent pressure Poisson equation
* consistent penalty methods
* consistent normal direction
* consistent heat flux
* consistent forces
Fully indexed and referenced, this book is an essential reference tool for all researchers, students and applied scientists in incompressible fluid mechanics.
Volume One provides extensive coverage of the prototypical fluid mechanics equation: the advectiondiffusion equation. For both this equation and the equations of principal interest  the NavierStokes equations (covered in detail in Volume Two)  a discussion of both the continuous and discrete equations is presented, as well as explanations of how to properly march the timedependent equations using smart implicit methods. Boundary and initial conditions, so important in applications, are carefully described and discussed, including wellposedness. The important role played by the pressure, so confusing in the past, is carefully explained.
The book explains and emphasizes consistency in six areas:
* consistent mass matrix
* consistent pressure Poisson equation
* consistent penalty methods
* consistent normal direction
* consistent heat flux
* consistent forces
Fully indexed and referenced, this book is an essential reference tool for all researchers, students and applied scientists in incompressible fluid mechanics.
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Glossary of Abbreviations
Preface and Introduction
3. The NavierStokes Equations
3.1 Notational Introduction
3.2 The Continuum Equations
3.3 Alternate Forms of the Viscous Term
3.4 Alternate Forms of the NonLinear Term
3.5 Derived Equations
3.6 Alternate Statements of the NS Equations
3.7 Special Cases of Interest
3.8 Boundary Conditions
3.9 Initial Conditions (and WellPosedness)
3.10 Interim Summary
3.11 Global Conservation Laws
3.12 Weak Form of the PDE's /
Natural Boundary Conditions (NBC's)
3.13 The Finite Element Equations /
Discretization of the Weak Form
3.14 A Control Volume Finite Element Method
3.15 Variational Principles for Potential and Stokes Flow
3.16 Solution Methods for the Semi_Discretized TimeDependent (and Steady) Equations
3.17 Aliasing and Aliasing Instability, Linear and NonLinear
3.18 A New Look at Two Old Finite Difference Methods
3.19 Numerical Example 
Implusive Start
3.20 Closure: Some Additional Remarks on the Pressure
4. Derived Quantities
4.1 Introduction
4.2 Two Dimensions
4.3 Three Dimensions
Appendix 1 Some Element Matrix
A.1.1 Advection Diffusion Matrices
A.1.2 OneDimensional Element Matrices
A.1.3 TwoDimensional Element Matrices
A.1.4 NavierStokes: Additional Matrices
A.1.5 TwoDimensional Control Volume Finite Element Matrices
Appendix 2 Further Comparison of Finite Elements and Finite
Volumes
A.2.1 Introduction
A.2.2 Viewpoint One
A.2.3 Viewpoint Two
Appendix 3 Projections, Orthagonal and Not and Projection Methods
A.3.1 Introduction
A.3.2 Scalar Projections
A.3.3 Vector Projections
References
Author Index
Subject Index
Preface and Introduction
3. The NavierStokes Equations
3.1 Notational Introduction
3.2 The Continuum Equations
3.3 Alternate Forms of the Viscous Term
3.4 Alternate Forms of the NonLinear Term
3.5 Derived Equations
3.6 Alternate Statements of the NS Equations
3.7 Special Cases of Interest
3.8 Boundary Conditions
3.9 Initial Conditions (and WellPosedness)
3.10 Interim Summary
3.11 Global Conservation Laws
3.12 Weak Form of the PDE's /
Natural Boundary Conditions (NBC's)
3.13 The Finite Element Equations /
Discretization of the Weak Form
3.14 A Control Volume Finite Element Method
3.15 Variational Principles for Potential and Stokes Flow
3.16 Solution Methods for the Semi_Discretized TimeDependent (and Steady) Equations
3.17 Aliasing and Aliasing Instability, Linear and NonLinear
3.18 A New Look at Two Old Finite Difference Methods
3.19 Numerical Example 
Implusive Start
3.20 Closure: Some Additional Remarks on the Pressure
4. Derived Quantities
4.1 Introduction
4.2 Two Dimensions
4.3 Three Dimensions
Appendix 1 Some Element Matrix
A.1.1 Advection Diffusion Matrices
A.1.2 OneDimensional Element Matrices
A.1.3 TwoDimensional Element Matrices
A.1.4 NavierStokes: Additional Matrices
A.1.5 TwoDimensional Control Volume Finite Element Matrices
Appendix 2 Further Comparison of Finite Elements and Finite
Volumes
A.2.1 Introduction
A.2.2 Viewpoint One
A.2.3 Viewpoint Two
Appendix 3 Projections, Orthagonal and Not and Projection Methods
A.3.1 Introduction
A.3.2 Scalar Projections
A.3.3 Vector Projections
References
Author Index
Subject Index
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