Riemann solvers and numerical methods for fluid dynamics : a practical introduction
著者
書誌事項
Riemann solvers and numerical methods for fluid dynamics : a practical introduction
Springer, c1997
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内容説明・目次
内容説明
High resolution upwind and centered methods are now a mature generation of computational techniques applicable to a range of engineering and scientific disciplines, with computational fluid dynamics being the most prominent. This textbook gives a practical presentation of this class of techniques. It is designed to provide readers with an understanding of the basic concepts, some of the underlying theory, the ability to use research papers on the subject, and, above all, with the required information for the practical implimentation of the methods. Applications include: compressible; steady; unsteady; reactive; viscous; non-viscous; and free surface flows. The author takes a didactic approach and points out practical applications. The book also contains some sample FORTRAN programs.
目次
- Governing equations
- mathematical preliminaries
- some properties of the Euler equations
- the Riemann problem for the Euler equations
- notions on numerical methods
- the method of Godunov for non-linear systems
- random choice and related methods
- the flux vector splitting approach
- approximate-state Riemann solvers
- HLL-type Rieman Solvers
- the Riemann solver of Roe
- the Riemann solver of Osher
- TVD methods for scalar problems
- TVD methods for non-linear systems
- schemes for source terms
- methods for multi-dimensional problems
- the shallow water equations
- problems for the Navier-Stokes equations
- the Riemann problem for general materials
- selected topics.
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