Call number:
AWI S3-01-0032
In:
Texts in applied mathematics
Description / Table of Contents:
Contents: Series Preface. - Preface. - 1 Introduction. - 2 Basic finite-difference methods. - 3 Beyond the one-way wave equation. - 4 Series-expansion methods. - 5 Finite volume methods. - 6 Semi-lagrangian methods. - 7 Physically insignificant fast waves. - 8 Nonreflecting boundary conditions. - Appendix. - Bibliography. - Index
Description / Table of Contents:
This scholarly text provides an introduction to the numerical methods used to model partial differential equations governing wave-like and weakly dissipative flows. The focus of the book is on fundamental methods and standard fluid dynamical problems such as tracer transport, the shallow-water equations, and the Euler equations. The emphasis is on methods, appropriate for applications in atmospheric and oceanic science, but these same methods are also well suited for the simulation of wave-like flows in many other scientific and engineering disciplines. The text discusses finite-difference, spectral, finite-element, and finite-volume methods. Also included are additional chapters on semi-Lagrangian schemes, nonreflecting boundary conditions, and methods for the efficient solution of problems that include physically insignificant rapidly propagating waves. Throughout the book the author has followed a middle course between the theorem-proof formalism of a pre mathematics text and the highly empirical approach found in some engineering publications. Although there are no formal proofs, the essential characteristics of the various schemes are mathematically derived in a style familiar to physical scientists. Numerical examples illustrating the theoretically derived properties of the various methods are presented throughout the book to establish a concrete link between theory and practice. Both theoretical and applied problems are provided at the end of each chapter. Numerical methods for wave equations in geophysical fluid dynamics will be useful as a senior and undergraduate and graduate text, and as a reference for those teaching or using numerical methods, particulary for those concentrating on fluid dynamics.
Type of Medium:
Monograph available for loan
Pages:
XVII, 465 S. : graph. Darst.
ISBN:
0387983767
Series Statement:
Texts in applied mathematics 32
Branch Library:
AWI Library
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