Incompressible Flow and the Finite Element Method Incompressible Flow and the Finite Element Method This comprehensive two-volume 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 advection-diffusion equation. For both this equation and the equations of principal interest - the Navier-Stokes 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 time-dependent equations using smart implicit methods. Boundary and initial conditions, so important in applications, are carefully described and discussed, including well-posedness. 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. John Wiley & Sons, Inc 978-0-471-49250-4
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Incompressible Flow and the Finite Element Method

  • Автор: P.M. Gresho, R.L. Sani
  • Мягкий переплет. Крепление скрепкой или клеем
  • Издательство: John Wiley & Sons, Inc
  • Год выпуска: 2000
  • Кол. страниц: 632
  • ISBN: 978-0-471-49250-4
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This comprehensive two-volume 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 advection-diffusion equation. For both this equation and the equations of principal interest - the Navier-Stokes 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 time-dependent equations using smart implicit methods. Boundary and initial conditions, so important in applications, are carefully described and discussed, including well-posedness. 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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Содержание
Glossary of Abbreviations
Preface and Introduction
3. The Navier-Stokes Equations
3.1 Notational Introduction
3.2 The Continuum Equations
3.3 Alternate Forms of the Viscous Term
3.4 Alternate Forms of the Non-Linear 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 Well-Posedness)
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 Time-Dependent (and Steady) Equations
3.17 Aliasing and Aliasing Instability, Linear and Non-Linear
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 One-Dimensional Element Matrices
A.1.3 Two-Dimensional Element Matrices
A.1.4 Navier-Stokes: Additional Matrices
A.1.5 Two-Dimensional 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
Штрихкод:   9780471492504
Аудитория:   Для специалистов
Бумага:   Офсет
Масса:   645 г
Размеры:   245x 170x 39 мм
Оформление:   Частичная лакировка
Тираж:   3 000
Литературная форма:   Справочное издание, Учебное пособие
Тип иллюстраций:   Черно-белые
Составитель:   Sani R.L.
Язык:   Английский
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