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.
Inhaltsverzeichnis
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.
