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Donea, Jean / Huerta, Antonio
Finite Element Methods for Flow Problems

1. Edition April 2003
139.- Euro
2003. 362 Pages, Hardcover
- Textbook -
ISBN 978-0-471-49666-3 - John Wiley & Sons



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Short description
In recent years, there have been a number of advances in the development of stable and accurate finite element procedures for approximating numerically a wide range of fluid mechanics problems. Taking an engineering rather than a mathematical approach, the Finite Element Method details the fundamentals of stabilized finite element methods for analyzing steady and time-dependent fluid mechanics problems. Characterized by a simplicity of presentation, the book's topical range reaches the forefront of current research in several areas of computational fluid dynamics.

From the contents
Preface.

1. Introduction and preliminaries.

Finite elements in fluid dynamics.

Subjects covered.

Kinematical descriptions of the flow field.

The basic conservation equations.

Basic ingredients of the finite element method.

2. Steady transport problems.

Problem statement.

Galerkin approximation.

Early Petrov-Galerkin methods.

Stabilization techniques.

Other stabilization techniques and new trends.

Applications and solved exercises.

3. Unsteady convective transport.

Introduction.

Problem statement.

The methods of characteristics.

Classical time and space discretization techniques.

Stability and accuracy analysis.

Taylor-Galerkin Methods.

An introduction to monotonicity-preserving schemes.

Least-squares-based spatial discretization.

The discontinuous Galerkin method.

Space-time formulations.

Applications and solved exercises.

4. Compressible Flow Problems.

Introduction.

Nonlinear hyperbolic equations.

The Euler equations.

Spatial discretization techniques.

Numerical treatment of shocks.

Nearly incompressible flows.

Fluid-structure interaction.

Solved exercises.

5. Unsteady convection-diffusion problems.

Introduction.

Problem statement.

Time discretization procedures.

Spatial discretization procedures.

Stabilized space-time formulations.

Solved exercises.

6. Viscous incompressible flows.

Introduction

Basic concepts.

Main issues in incompressible flow problems.

Trial solutions and weighting functions.

Stationary Stokes problem.

Steady Navier-Stokes problem.

Unsteady Navier-Stokes equations.

Applications and Solved Exercices.

References.

Index.

 





 

        

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