Numerical Computation of Internal and External Flows, Volume 1: Fundamentals of Numerical Discretization

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