Finite Element Methods for Flow Problems
1. Edition April 2003
362 Pages, Hardcover
Textbook
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.
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.
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.
