Ebook: Computational Aerodynamics and Fluid Dynamics: An Introduction

This textbook is written for senior undergraduate and graduate students as well as engineers who will develop or use code in the simulation of fluid flows or other physical phenomena. The objective of the book is to give the reader the basis for understanding the way numerical schemes achieve accurate and stable simulations of physical phenomena. It is based on the finite-difference method and simple enough problems that allow also the analytic solutions to be worked out. ODEs as well as hyperbolic, parabolic and elliptic types are treated. The reader also will find a chapter on the techniques of linearization of nonlinear problems. The final chapter applies the material to the equations of gas dynamics. The book builds on simple model equations and, pedagogically, on a host of problems given together with their solutions.

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This textbook is written for senior undergraduate and graduate students as well as engineers who will develop or use code in the simulation of fluid flows or other physical phenomena. The objective of the book is to give the reader the basis for understanding the way numerical schemes achieve accurate and stable simulations of physical phenomena. It is based on the finite-difference method and simple enough problems that allow also the analytic solutions to be worked out. ODEs as well as hyperbolic, parabolic and elliptic types are treated. The reader also will find a chapter on the techniques of linearization of nonlinear problems. The final chapter applies the material to the equations of gas dynamics. The book builds on simple model equations and, pedagogically, on a host of problems given together with their solutions.

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This textbook is written for senior undergraduate and graduate students as well as engineers who will develop or use code in the simulation of fluid flows or other physical phenomena. The objective of the book is to give the reader the basis for understanding the way numerical schemes achieve accurate and stable simulations of physical phenomena. It is based on the finite-difference method and simple enough problems that allow also the analytic solutions to be worked out. ODEs as well as hyperbolic, parabolic and elliptic types are treated. The reader also will find a chapter on the techniques of linearization of nonlinear problems. The final chapter applies the material to the equations of gas dynamics. The book builds on simple model equations and, pedagogically, on a host of problems given together with their solutions.
Content:
Front Matter....Pages I-XI
Introduction....Pages 1-3
Basics of the Finite-Difference Method....Pages 5-17
Application to the Integration of Ordinary Differential Equations....Pages 19-26
Partial Differential Equations....Pages 27-39
Integration of a Linear Hyperbolic Equation....Pages 41-52
Integration of a Linear Parabolic Equation....Pages 53-62
Integration of a Linear Elliptic Equation....Pages 63-74
Finite Difference Scheme for a Convection-Diffusion Equation....Pages 75-80
The Method of Murman and Cole....Pages 81-92
Treatment of Non-Linearities....Pages 93-100
Application to a System of Equations....Pages 101-112
Back Matter....Pages 113-186

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This textbook is written for senior undergraduate and graduate students as well as engineers who will develop or use code in the simulation of fluid flows or other physical phenomena. The objective of the book is to give the reader the basis for understanding the way numerical schemes achieve accurate and stable simulations of physical phenomena. It is based on the finite-difference method and simple enough problems that allow also the analytic solutions to be worked out. ODEs as well as hyperbolic, parabolic and elliptic types are treated. The reader also will find a chapter on the techniques of linearization of nonlinear problems. The final chapter applies the material to the equations of gas dynamics. The book builds on simple model equations and, pedagogically, on a host of problems given together with their solutions.
Content:
Front Matter....Pages I-XI
Introduction....Pages 1-3
Basics of the Finite-Difference Method....Pages 5-17
Application to the Integration of Ordinary Differential Equations....Pages 19-26
Partial Differential Equations....Pages 27-39
Integration of a Linear Hyperbolic Equation....Pages 41-52
Integration of a Linear Parabolic Equation....Pages 53-62
Integration of a Linear Elliptic Equation....Pages 63-74
Finite Difference Scheme for a Convection-Diffusion Equation....Pages 75-80
The Method of Murman and Cole....Pages 81-92
Treatment of Non-Linearities....Pages 93-100
Application to a System of Equations....Pages 101-112
Back Matter....Pages 113-186
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