High accuracy non-centered compact difference schemes for fluid dynamics applications
著者
書誌事項
High accuracy non-centered compact difference schemes for fluid dynamics applications
（Series on advances in mathematics for applied sciences, vol.21）
World Scientific, c1994
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内容説明・目次
内容説明
This is the first book which describes completely the nontraditional difference schemes which combine the ideas of Padé-type approximation and upwind differencing. These possess some favorable properties and can be used to solve various problems in fluid dynamics and related disciplines. They were proposed by the author in the seventies and are extensively used in Russia. However, they seem to be relatively unknown outside the country. In this book, the author presents the theory of the schemes, to provide some sophisticated algorithms for different computational fluid dynamics problems, to supply readers with useful information which would permit them to construct a rich variety of algorithms of this type and to illustrate the applications of these methods to the numerical simulation of various fluid dynamics phenomena, ranging from supersonic viscous flows to some atmosphere and ocean processes. This book is an essential guide for anyone keenly interested in this field.
目次
- Third-order schemes with compact upwind differencing
- some extensions of basic ideas
- fifth-order non-centred compact schemes
- hyperbolic systems
- compact upwind schemes for convection diffusion equations
- multidimensional problems
- applications to compressible gas flows
- application of compact approximations to incompressible flow problems
- solution-dependent co-ordinate transformations for adaptive mesh generation
- some relevant mathematical topics.
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