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" Computational Techniques for Fluid Dynamics 1 "
by Clive A. J. Fletcher.
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BL
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578539
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b407758
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| Main Entry
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Fletcher, Clive A. J.
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| Title & Author
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Computational Techniques for Fluid Dynamics 1 : Fundamental and General Techniques /\ by Clive A. J. Fletcher.
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| Publication Statement
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Berlin, Heidelberg :: Springer Berlin Heidelberg :: Imprint: Springer,, 1988.
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| Series Statement
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Springer Series in Computational Physics
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| ISBN
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9783642970351
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: 9783642970375
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| Contents
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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 -- A.1 Empirical Determination of the Execution Time of Basic Operations -- A.2 Mass and Difference Operators -- References.
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| Abstract
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The purpose of this two-volume textbook is to provide students of engineer ing, science and applied mathematics with the specific techniques, and the framework to develop skill in using them, that have proven effective in the various branches of computational fluid dynamics (CFD). Volume 1 de scribes both fundamental and general techniques that are relevant to all branches of fluid flow. Volume 2 provides specific techniques, applicable to the different categories of engineering flow behaviour, many of which are also appropriate to convective heat transfer. An underlying theme of the text ist that the competing formulations which are suitable for computational fluid dynamics, e.g. the finite differ ence, finite element, finite volume and spectral methods, are closely related and can be interpreted as part of a unified structure. Classroom experience indicates that this approach assists, considerably, the student in acquiring a deeper understanding of the strengths and weaknesses of the alternative computational methods. Through the provision of 24 computer programs and associated exam ples and problems, the present text is also suitable for established research workers and practitioners who wish to acquire computational skills without the benefit of formal instruction. The text includes the most up-to-date techniques and is supported by more than 300 figures and 500 references.
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| Subject
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Physics.
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Mathematical physics.
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SpringerLink (Online service)
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