The purpose and organisation ofthis book are described in the preface to the first edition (1988). In preparing this edition minor changes have been made, par ticularly to Chap. 1to keep it reasonably current. However, the rest of the book has required only minor modification to clarify the presentation and to modify or replace individual problems to make them more effective. The answers to the problems are available in Solutions Manual for Computational Techniques for Fluid DynamicsbyC. A. 1. Fletcherand K. Srinivas, published by Springer-Verlag, Heidelberg, 1991. The computer programs have also been reviewed and tidied up. These are available on an IBM-compatible floppy disc direct from the author. I would like to take this opportunityto thank the many readers for their usually generous comments about the first edition and particularly those readers who went to the trouble of drawing specific errors to my attention. In this revised edi tion considerable effort has been made to remove a number of minor errors that had found their way into the original. I express the hope that no errors remain but welcome communication that will help me improve future editions. In preparing this revised edition I have received considerable help from Dr. K. Srinivas, Nam-Hyo Cho, Zili Zhu and SusanGonzales at the UniversityofSydney and from Professor W. BeiglbOck and his colleagues at Springer-Verlag. I am very grateful to all of them.
Inhaltsverzeichnis
1. Computational Fluid Dynamics: An Introduction. - 1. 1 Advantages of Computational Fluid Dynamics. - 1. 2 Typical Practical Problems. - 1. 3 Equation Structure. - 1. 4 Overview of Computational Fluid Dynamics. - 1. 5 Further Reading. - 2. Partial Differential Equations. - 2. 1 Background. - 2. 2 Hyperbolic Partial Differential Equations. - 2. 3 Parabolic Partial Differential Equations. - 2. 4 Elliptic Partial Differential Equations. - 2. 5 Traditional Solution Methods. - 2. 6 Closure. - 2. 7 Problems. - 3. Preliminary Computational Techniques. - 3. 1 Discretisation. - 3. 2 Approximation to Derivatives. - 3. 3 Accuracy of the Discretisation Process. - 3. 4 Wave Representation. - 3. 5 Finite Difference Method. - 3. 6 Closure. - 3. 7 Problems. - 4. Theoretical Background. - 4. 1 Convergence. - 4. 2 Consistency. - 4. 3 Stability. - 4. 4 Solution Accuracy. - 4. 5 Computational Efficiency. - 4. 6 Closure. - 4. 7 Problems. - 5. Weighted Residual Methods. - 5. 1 General Formulation. - 5. 2 Finite Volume Method. - 5. 3 Finite Element Method and Interpolation. - 5. 4 Finite Element Method and the Sturm-Liouville Equation. - 5. 5 Further Applications of the Finite Element Method. - 5. 6 Spectral Method. - 5. 7 Closure. - 5. 8 Problems. - 6. Steady Problems. - 6. 1 Nonlinear Steady Problems. - 6. 2 Direct Methods for Linear Systems. - 6. 3 Iterative Methods. - 6. 4 Pseudotransient Method. - 6. 5 Strategies for Steady Problems. - 6. 6 Closure. - 6. 7 Problems. - 7. One-Dimensional Diffusion Equation. - 7. 1 Explicit Methods. - 7. 2 Implicit Methods. - 7. 3 Boundary and Initial Conditions. - 7. 4 Method of Lines. - 7. 5 Closure. - 7. 6 Problems. - 8. Multidimensional Diffusion Equation. - 8. 1 Two-Dimensional Diffusion Equation. - 8. 2 Multidimensional Splitting Methods. - 8. 3 Splitting Schemes and the Finite Element Method. - 8. 4 Neumann Boundary Conditions. - 8. 5 Method of Fractional Steps. - 8. 6 Closure. - 8. 7 Problems. - 9. Linear Convection-Dominated Problems. - 9. 1 One-Dimensional Linear Convection Equation. - 9. 2 Numerical Dissipation and Dispersion. - 9. 3 Steady Convection-Diffusion Equation. - 9. 4 One-Dimensional Transport Equation. - 9. 5 Two-Dimensional Transport Equation. - 9. 6 Closure. - 9. 7 Problems. - 10. Nonlinear Convection-Dominated Problems. - 10. 1 One-Dimensional Burgers Equation. - 10. 2 Systems of Equations. - 10. 3 Group Finite Element Method. - 10. 4 Two-Dimensional Burgers Equation. - 10. 5 Closure. - 10. 6 Problems. - Appendix A. 1 Empirical Determination of the Execution Time of Basic Operations. - A. 2 Mass and Difference Operators. - References.
