Ebook: Fundamentals of Computational Fluid Dynamics

This book is intended as a textbook for a first course in computational fluid dynamics and will be of interest to researchers and practitioners as well. It emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. The linear convection and diffusion equations are used to illustrate concepts throughout. The chosen approach, in which the partial differential equations are reduced to ordinary differential equations, and finally to difference equations, gives the book its distinctiveness and provides a sound basis for a deep understanding of the fundamental concepts in computational fluid dynamics.

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This book is intended as a textbook for a first course in computational fluid dynamics and will be of interest to researchers and practitioners as well. It emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. The linear convection and diffusion equations are used to illustrate concepts throughout. The chosen approach, in which the partial differential equations are reduced to ordinary differential equations, and finally to difference equations, gives the book its distinctiveness and provides a sound basis for a deep understanding of the fundamental concepts in computational fluid dynamics.

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This book is intended as a textbook for a first course in computational fluid dynamics and will be of interest to researchers and practitioners as well. It emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. The linear convection and diffusion equations are used to illustrate concepts throughout. The chosen approach, in which the partial differential equations are reduced to ordinary differential equations, and finally to difference equations, gives the book its distinctiveness and provides a sound basis for a deep understanding of the fundamental concepts in computational fluid dynamics.
Content:
Front Matter....Pages I-XIV
Introduction....Pages 1-5
Conservation Laws and the Model Equations....Pages 7-18
Finite-Difference Approximations....Pages 19-47
The Semi-Discrete Approach....Pages 49-65
Finite-Volume Methods....Pages 67-79
Time-Marching Methods for ODE’S....Pages 81-114
Stability of Linear Systems....Pages 115-140
Choosing a Time-Marching Method....Pages 141-152
Relaxation Methods....Pages 153-176
Multigrid....Pages 177-187
Numerical Dissipation....Pages 189-201
Split and Factored Forms....Pages 203-216
Analysis of Split and Factored Forms....Pages 217-230
Back Matter....Pages 231-249

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This book is intended as a textbook for a first course in computational fluid dynamics and will be of interest to researchers and practitioners as well. It emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. The linear convection and diffusion equations are used to illustrate concepts throughout. The chosen approach, in which the partial differential equations are reduced to ordinary differential equations, and finally to difference equations, gives the book its distinctiveness and provides a sound basis for a deep understanding of the fundamental concepts in computational fluid dynamics.
Content:
Front Matter....Pages I-XIV
Introduction....Pages 1-5
Conservation Laws and the Model Equations....Pages 7-18
Finite-Difference Approximations....Pages 19-47
The Semi-Discrete Approach....Pages 49-65
Finite-Volume Methods....Pages 67-79
Time-Marching Methods for ODE’S....Pages 81-114
Stability of Linear Systems....Pages 115-140
Choosing a Time-Marching Method....Pages 141-152
Relaxation Methods....Pages 153-176
Multigrid....Pages 177-187
Numerical Dissipation....Pages 189-201
Split and Factored Forms....Pages 203-216
Analysis of Split and Factored Forms....Pages 217-230
Back Matter....Pages 231-249
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