Computational Aerodynamics and Fluid Dynamics

1. Front Matter

   Pages I-XI

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2. Introduction

   • Jean-Jacques Chattot

   Pages 1-3

3. Basics of the Finite-Difference Method

   • Jean-Jacques Chattot

   Pages 5-17

4. Application to the Integration of Ordinary Differential Equations

   • Jean-Jacques Chattot

   Pages 19-26

5. Partial Differential Equations

   • Jean-Jacques Chattot

   Pages 27-39

6. Integration of a Linear Hyperbolic Equation

   • Jean-Jacques Chattot

   Pages 41-52

7. Integration of a Linear Parabolic Equation

   • Jean-Jacques Chattot

   Pages 53-62

8. Integration of a Linear Elliptic Equation

   • Jean-Jacques Chattot

   Pages 63-74

9. Finite Difference Scheme for a Convection-Diffusion Equation

   • Jean-Jacques Chattot

   Pages 75-80

10. The Method of Murman and Cole

    • Jean-Jacques Chattot

    Pages 81-92

11. Treatment of Non-Linearities

    • Jean-Jacques Chattot

    Pages 93-100

12. Application to a System of Equations

    • Jean-Jacques Chattot

    Pages 101-112

13. Back Matter

    Pages 113-186

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The field of computational fluid dynamics (CFD) has matured since the au­ thor was first introduced to electronic computation in the mid-sixties. The progress of numerical methods has paralleled that of computer technology and software. Simulations are used routinely in all branches of engineering as a very powerful means for understanding complex systems and, ultimately, improve their design for better efficiency. Today's engineers must be capable of using the large simulation codes available in industry, and apply them to their specific problem by implemen­ ting new boundary conditions or modifying existing ones. The objective of this book is to give the reader the basis for understanding the way numerical schemes achieve accurate and stable simulations of phy­ sical phenomena, governed by equations that are related, yet simpler, than the equations they need to solve. The model problems presented here are linear, in most cases, and represent the propagation of waves in a medium, the diffusion of heat in a slab, and the equilibrium of a membrane under distributed loads. Yet, regardless of the origin of the problem, the partial differential equations (PDE's) reflect the physical phenomena to be modeled and can be classified as being of hyperbolic, parabolic or elliptic type. The numerical treatment depends on the equation type that can represent several physical situations as diverse as heat conduction and viscous fluid flow. Non­ linear model problems are also presented and solved, such as the transonic small disturbance equation and the equations of gas dynamics.

• Aerodynamics
• Euler Method
• Finite Difference Method
• Fluid Flows
• Gas Dynamics
• Lax Scheme
• Mixed-Type Scheme
• Murman-Cole Method
• Runge-Kutta Method
• Stability of Numerical Schemes
• Upwind Scheme
• convection
• fluid dynamics
• simulation
• fluid- and aerodynamics

From the reviews:

"Most of the book is classical, i.e. the author carries out a clear and concise review of finite difference methods (explicit and implicit) used to integrate initial and/or boundary value problems for ordinary and partial differential equations. [...] However, it is the appendix devoted to problems, which confers a distinctive position on this book in the CFD literature. The author works out in detail ten nontrivial problems in a very pedagogical manner." (Zentralblatt MATH, 1013, 2003)

"[...] a very well-written book. This reviewer recommends it highly for advanced undergraduate and first-year graduate classes. In addition, engineers and scientists interested in numerical simulation of fluid flow and plasma flow should find this an excellent self-study textbook." (Shi Tsan Wu, Applied Mechanics Reviews, 56/3, 2003)

"The objective of the textbook is to give the reader the basic knowledge in using numerical knowledge in using numerical methods for an accurate and stable simulation of physical phenomena in aerodynamics and fluid dynamics. The general idea of the book is to motivate the reader to write his own code and to use it in application. … The book is well suited for senior undergraduate, first year graduate students, and engineers who will be developing or using codes in CFD based on finite differences." (Lutz Tobiska, Mathematical Reviews, Issue 2004 d)

"The author carries out a clear and concise review of finite difference methods (explicit and implicit) used to integrate initial and/or boundary value problems for ordinary and partial differential equations. Practical aspects of the implementation of some selected schemes are also considered. … it is the appendix devoted to problems, which confers a distinctive position on this book in the CFD literature." (Calin Ioan Gheorghiu, Zentralblatt MATH, Vol. 1013, 2003)

"In this book, the author has documented his lecture notes on computational fluiddynamics (CFD) … . The most significant aspect of this book is that the author presents two appendices that include the problems and solutions, respectively. … Computational Aerodynamics and Fluid Dynamics: An Introduction is a very well-written book. This reviewer recommends it highly for advanced under-graduate and first-year graduate classes. In addition, engineers and scientists interested in numerical simulation of fluid flow and plasma flow should find this an excellent self-study book." (Shi Tsan Wu, Applied Mechanics Reviews, Vol. 56 (3), 2003)

• Department of Mechanical and Aeronautical Engineering, University of California, Davis, USA

  Jean-Jacques Chattot

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