Book description
Finite Element Techniques for Fluid Flow describes the advances in the applications of finite element techniques to fluid mechanics. Topics covered range from weighted residual and variational methods to interpolation functions, inviscid fluids, and flow through porous media. The basic principles and governing equations of fluid mechanics as well as problems related to dispersion and shallow water circulation are also discussed. This text is comprised of nine chapters; the first of which explains some basic definitions and properties as well as the basic principles of weighted residual and variational methods. The reader is then introduced to the simple finite element concepts and models, and gradually to more complex applications. The chapters that follow focus on the governing equations of fluid flow, the solutions to potential type problems, and viscous flow problems in porous media. The solutions to more specialized problems are also presented. This book also considers how circulation problems can be tackled using finite elements, presents a solution to the mass transfer equation, and concludes with an explanation of how to solve general transient incompressible flows. This source will be of use to engineers, applied mathematicians, physicists, self-taught students, and research workers.
Table of contents
- Front Cover
- Finite Element Techniques for Fluid Flow
- Copyright Page
- Table of Contents
- Preface
-
Chapter 1. Weighted Residual and Variational Methods
- 1.1 Basic definitions
- 1.2 Weighted residual methods (1/3)
- 1.2 Weighted residual methods (2/3)
- 1.2 Weighted residual methods (3/3)
- 1.3 Weak formulations (1/3)
- 1.3 Weak formulations (2/3)
- 1.3 Weak formulations (3/3)
- 1.4 Initial value problems (1/2)
- 1.4 Initial value problems (2/2)
- 1.5 The case of quadratic functional
- 1.6 Rayleigh–Ritz method
- 1.7 Subsidiary conditions
- BIBLIOGRAPHY
- EXERCISES
- Chapter 2. The Finite Element Technique
-
Chapter 3. Interpolation Functions
- 3.1 Introduction
- 3.2 First-order continuity functions for triangular elements (1/3)
- 3.2 First-order continuity functions for triangular elements (2/3)
- 3.2 First-order continuity functions for triangular elements (3/3)
- 3.3 First-order continuity functions for rectangular elements (1/2)
- 3.3 First-order continuity functions for rectangular elements (2/2)
- 3.4 Isoparametric elements
- 3.5 Second-order continuity functions for rectangular elements (1/2)
- 3.5 Second-order continuity functions for rectangular elements (2/2)
- 3.6 Second-order continuity functions for triangular elements (1/2)
- 3.6 Second-order continuity functions for triangular elements (2/2)
- REFERENCES
- EXERCISES
-
Chapter 4. Basic Principles and Governing Equations of Fluid Mechanics
- 4.1 Eulerian and Lagrangian formulations: material derivative
- 4.2 Deformation rate measures
- 4.3 Equilibrium equations
- 4.4 The energy equation
- 4.5 Constitutive equations—Newtonian fluid
- 4.6 Navier–Stokes equations—incompressible Newtonian fluid
- 4.7 The principle of virtual power
- 4.8 Turbulence
- BIBLIOGRAPHY
- EXERCISES
- Chapter 5. Inviscid Fluids
- Chapter 6. Flow Through Porous Media
- Chapter 7. Shallow Water Circulation Problems
- Chapter 8. Dispersion Problems
- Chapter 9. Viscous Incompressible Flow Problems
- Appendix: Numerical integration formulae
- Index
Product information
- Title: Finite Element Techniques for Fluid Flow
- Author(s):
- Release date: September 2013
- Publisher(s): Newnes
- ISBN: 9781483161167
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