Description
Book SynopsisTaking 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.
Trade Review“…essential reading for graduate students and researchers in engineering and applied sciences..” (CAB Abstracts)
Table of ContentsPreface.
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.
