CiNii 図書 - Fundamentals of numerical discretization

The first of two volumes giving a comprehensive account 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 the various methods, so the reader can see which would be the most appropriate way of solving any particular problem. In the first part of the book, mathematical models are introduced; in the second part, the various numerical methods are described briefly; in the third and fourth parts, the workings of these methods are discussed in more detail.

THE MATHEMATICAL MODELS FOR FLUID FLOW SIMULATIONS AT VARIOUS LEVELS OF APPROXIMATION: Introduction
The Basic Equations of Fluid Dynamics
The Dynamical Levels of Approximation
The Mathematical Nature of the Flow Equations and Their Boundary Conditions
BASIC DISCRETIZATION TECHNIQUES: The Finite Difference Method
The Finite Element Method
Finite Volume Method and Conservative Discretizations
THE ANALYSIS OF NUMERICAL SCHEMES: The Concepts of Consistency, Stability and Convergence
The Von Neumann Method for Stability Analysis
The Method of the Equivalent Differential Equation for the Analysis of Stability
The Matrix Method for Stability Analysis
THE RESOLUTION OF DISCRETIZED EQUATIONS: Integration Methods for Systems of Ordinary Differential Equations
Iterative Methods for the Resolution of Algebraic Systems.

巻冊次: : pbk ISBN 9780471923855

内容説明

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

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Fundamentals of numerical discretization

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