Incompressible Flow and the Finite Element Method, Advection-Diffusion and Isothermal Laminar Flow / Edition 1

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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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Editorial Reviews

Acknowledging that the use of the finite element method is one of the more difficult topics in the field of computational fluid dynamics, the authors' hope to present an overview that will allow engineers and others turned off by the complicated math to grasp the essentials of the topic. This is done by presenting a relatively uncluttered explanation of the finite element method and by presenting and interpreting the final discrete equations in the form of simple finite difference equations. This volume only deals with advection and diffusion, while the next volume will treat isothermal laminar flow. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780471492498
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 6/30/2000
  • Edition number: 1
  • Pages: 480
  • Product dimensions: 6.65 (w) x 9.65 (h) x 0.94 (d)

Table of Contents

Preface Glossary of Abbreviations
1. Introduction
1.1 Introduction
1.2 Incompressible Flow
1.3 The Finite Element Method
1.4 Incompressible Flow and the Finite Element Method
1.5 Overview of this Volume
1.6 Some Subjective Discussion
1.7 Why Finite Elements? Why Not Finite Volumes?
2. The Advection-Diffusion Equation
2.1 The Continuum Equation
2.2 The Finite Element Equations /
Discretization of the Weak Form
2.3 Some Semi-Discrete Equations
2.4 Open Boundary Conditions (OBC's)
2.5 Some Non-Galerkin Results
2.6 Dispersion, Dissipation, Phase Speed, Group Velocity, Mesh Design, and Wiggles
2.7 Time Integration
2.8 Additional Numerical Examples Appendix 1 Some Element Matrices A.1.1 Advection Diffusion Matrices A.1.2 One-Dimensional Element Matrices A.1.3 Two-Dimensional Element Matrices A.1.4 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 Scalar Projections, Orthogonal and Not and Projection Methods A.3.1 Introduction A.3.2 Scalar Projections References Author Index Subject Index

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