Numerical Computation of Internal and External Flows, Volume 1

Numerical 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 practitioners and researchers working in computational fluid mechanics and dynamics.

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

Charles Sidney Hirsch was an American forensic pathologist who served as the Chief Medical Examiner of New York City from 1989 until 2013. He oversaw the identification of victims from the World Trade Center attacks in 2001.

Numerical 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 practitioners and researchers working in computational fluid mechanics and dynamics. 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