Numerical Methods for Fluid Dynamics: With Applications to Geophysics

by Dale R. Durran

Publisher: Springer Verlag
ISBN: 1441964118

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Book Description

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, non-reflecting 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 ground between the theorem-proof formalism of a pure 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 Fluid Dynamics will be useful as a senior undergraduate and graduate text and as a reference for those teaching or using numerical methods, particularly for those concentrating on fluid dynamics.

Dale R. Durran is a professor at the University of Washington, Seattle. He has a doctorate in meteorology from the Massachusetts Institute of Technology and a master's in mathematics from UC Berkeley.

From the Publisher

This is a well-written and interesting book on the numerical methods for nonlinear waves, concetrating on the atmospheric and oceanic sciences. It fills a real niche in the market. Lecturers and researchers in math, computer science, and geophysical sciences wanting an introduction to the numerical methods used in waves should be interested in this book.

From The Reviews

• "...The book's unquestionable advantage is the clarity and simplicity in presenting virtually all basic ideas and methods of numerical analysis currently actively used in geophysical fluid dynamics." - Physics of Atmosphere and Ocean "
• ...an excellent reference...should be brought to the attention of readers in meteorology, oceanography, physics, mechanics and engineering... an excellent text book...the extensiveness, theoretical and practical extent this book reaches make it a classical work." - Acta Meteorologica Sinica

Customer Reviews

In this introductory text space is equally divided into traditional methods (finite difference and spectral) and more modern methods (finite volume and semi-Lagrangian) for solving GFD-related PDEs. The book also contains chapters on filtering of physically insignificant fast waves and on open boundary conditions. Arguably these subjects can be learned by studying a collection of specialty books, but very seldom one finds even-handed treatment of all major techniques in a single book like this. More important, the breadth in scope does not come at the cost of depth or conciseness in presentation. Rather, the book achieves a delightful balance between breadth and depth, as well as between theory and practice. Not only is it an important successer to the long-respected Haltiner and Williams (1984), but it is much more readable.

I used the book to teach a graduate course on numerical methods at the University of Chicago. I could not cover the entire book in a 10-week quarter, but was able to cover chapters 2,3,4 and 5. The clearly written text was very helpful in organizing the class material.

The problems sets at the end of each chapter are also well designed, albeit mostly theoretical. It would be helpful to have separate programming assignments based on these problems, so students can learn how to apply principles into practice.