Finite Element Methods for Flow Problems

In recent years there have been significant developments in the development of stable and accurate finite element procedures for the numerical approximation of a wide range of fluid mechanics problems. Taking an engineering rather than a mathematical bias, this valuable reference resource details the fundamentals of stabilised finite element methods for the analysis of steady and time-dependent fluid dynamics problems. Organised into six chapters, this text combines theoretical aspects and practical applications and offers coverage of the latest research in several areas of computational fluid dynamics.
* Coverage includes new and advanced topics unavailable elsewhere in book form
* Collection in one volume of the widely dispersed literature reporting recent progress in this field
* Addresses the key problems and offers modern, practical solutions
Due to the balance between the concise explanation of the theory and the detailed description of modern practical applications, this text is suitable for a wide audience including academics, research centres and government agencies in aerospace, automotive and environmental engineering.Die Finite-Elemente-Methode, eines der wichtigsten in der Technik verwendeten numerischen Näherungsverfahren, wird hier gründlich und gut verständlich, aber ohne ein Zuviel an mathematischem Formalismus abgehandelt. Insbesondere geht es um die Anwendung der Methode auf Strömungsprobleme. Alle wesentlichen aktuellen Forschungsergebnisse wurden in den Band aufgenommen; viele davon sind bisher nur verstreut in der Originalliteratur zu finden. 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. “…essential reading for graduate students and researchers in engineering and applied sciences..” (CAB Abstracts)

Jean Donea is the author of Finite Element Methods for Flow Problems, published by Wiley.

Antonio Huerta is the author of Finite Element Methods for Flow Problems, published by Wiley. 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.