Description
Book SynopsisNumerical Computation of Internal and External Flows Volume 1: Fundamentals of Numerical Discretization
C. Hirsch, Vrije Universiteit Brussel, Brussels, Belgium
This is the first of two volumes which together describe comprehensively the theory and practice of the numerical computation of internal and external flows. In this volume, the author explains the use of basic computational methods to solve problems in fluid dynamics, comparing these methods so that the reader can see which would be the most appropriate to use for a particular problem. The book is divided into four parts. In the first part, mathematical models are introduced. In the second part, the various numerical methods are described, while in the third and fourth parts the workings of these methods are investigated in some detail.
Volume 2 will be concerned with the applications of numerical methods to flow problems, and together the two volumes will provide an excellent reference for
Table of Contents
Preface
Nomenclature
Part 1 The Mathematical Models for Fluid Flow Simulations at Various Levels of Approximation Introduction
Chapter 1 The Basic Equations of Fluid Dynamics
Chapter 2 The Dynamic Levels of Approximation
Chapter 3 The Mathematical Nature of the Flow Equations and their Boundary Conditions
Part II Basic Discretization Techniques
Chapter 4 The Finite Difference Method
Chapter 5 The Finite Element Method
Chapter 6 Finite Volume Method and Conservative Discretizations
Part III The Analysis of Numerical Schemes
Chapter 7 The Concepts of Consistency, Stability and Convergence
Chapter 8 The Von Neumann Method for Stability Analysis
Chapter 9 The Method of the Equivalent Differential Equation for the Analysis of Stability
Chapter 10 The Matrix Method for Stability Analysis
Part IV The Resolution of Discretized Equations
Chapter 11 Integration Methods for Systems of Ordinary Differential Equations
Chapter 12 Iterative Methods for the Resolution of Algebraic Systems
Appendix Thomas Algorithm for Tridiagonal Systems
Index
