Computational Techniques for Fluid Dynamics 1

From the reviews "In summary, a book of considerable utlity both in the classroom and as a reference volume ... Fletcher's book is sure to become an invaluable tool for student and researcher alike, and a trusted introduction and guide to the rapidly evolving field of CFD." (H. Aref in: Journal of Fluid Mechanics)

• 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.