Finite Element Methods for Flow Problems

Jean Donea, Antonio Huerta

360 pages, parution le 22/04/2003

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Résumé

Taking an engineering, rather than a mathematical, approach, Finite Element Methods for Flow Problems presents the fundamentals of stabilized finite element methods of the Petrov-Galerkin type developed as an alternative to the standard Galerkin method for the analysis of steady and time-dependent problems. The material presented here epitomizes the forefront of current research in several areas of computational fluid dynamics and combines theoretical aspects and practical applications.

Coverage includes:

Steady and transient convection-diffusion problems.
Stabilization techniques designed to produce stable and accurate results in convection-dominated situations.
The presentation and detailed analysis of high-order accurate time-stepping schemes for tracing the response of truly transient problems.
Special methods for purely convective transport governed by linear equations
Modelling of non-linear problems governed by the Euler equations of gas dynamics and the Navier-Stokes equations for viscous incompressible flows.
Spatial discretization by means of the arbitrary Lagrangian-Eulerian description with application to fluid-structure systems.
Worked examples.

The book provides essential reading for graduate students and researchers in engineering and applied sciences in the finite element field. The book will also be of interest to professionals working in aerospace, automotive, civil, environmental and offshore engineering, and safety technology.

Contents

Introduction and preliminaries

Finite elements in fluid dynamics
Subjects covered
Kinematical descriptions of the flow field
The basic conversion equations
Basic ingredients of the finite element method

Steady transport problems

Problem statement
Galerkin approximation
Early Petrov-Galerkin methods
Stabilization techniques
Other stabilization techniques and new trends
Applications and solved exercises

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

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

Unsteady convection-diffusion problems

Introduction
Problem statement
Time discretization procedures
Spatial discretization procedures
Stabilized space-time formulations
Solved exercises

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 exercises

References
Index

L'auteur - Jean Donea

Institut de Mécanique, université de Liège, Belgium.

L'auteur - Antonio Huerta

Departament de Matematica Aplicada III, Universitat Politecnica de Catalunya, Spain.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	Jean Donea, Antonio Huerta
Parution	22/04/2003
Nb. de pages	360
Format	15,5 x 23,5
Couverture	Relié
Poids	700g
Intérieur	Noir et Blanc
EAN13	9780471496663
ISBN13	978-0-471-49666-3