Numerical Methods for Fluid Dynamics: With Applications to Geophysics

ISBN-13: 9781461426851 / Angielski / Miękka / 2012 / 516 str.

Dale R. Durran

Opis

This scholarly text provides an introduction to the numerical methods used to model partial differential equations, with focus on atmospheric and oceanic flows. The book covers both the essentials of building a numerical model and the more sophisticated techniques that are now available. Finite difference methods, spectral methods, finite element method, flux-corrected methods and TVC schemes are all discussed. Throughout, the author keeps to a middle ground between the theorem-proof formalism of a mathematical text and the highly empirical approach found in some engineering publications. The book establishes a concrete link between theory and practice using an extensive range of test problems to illustrate the theoretically derived properties of various methods. From the reviews: ..".the books 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

Recenzje

From the reviews of the second edition:

"This is a largely self-contained and relatively far-reaching presentation of numerical fluid dynamics. It is aimed towards practitioners (meteorologists, physicists, engineers), providing ... a presentation of more mathematical depth than is frequently encountered in such books." (H. Muthsam, Monatshefte für Mathematik, Vol. 166 (1), April, 2012)

"Durran's direct and yet information-rich style makes this an excellent reference book. ... This is a good book for postdocs and professors as well as students. ... For an atmospheric modeler, this is probably the first book to buy. ... book is a more direct path to algorithms for graduate students and researchers who already have some familiarity with atmospheric dynamics. ... is worth a look by computational fluid dynamicists in other fields, especially those looking for ideas and insights outside their own particular specialties." (SIAM Review, Vol. 54 (4), 2012)

"This book is an introduction to numerical methods for fluid dynamics. ... The text could be useful to graduate students and scientists working in various branches of applied mathematics and engineering, not only in geophysical fluids. The material is intelligible to readers with a general mathematical background. The book includes exercises and is well illustrated with figures linking theoretical analyses to actual computations." (Titus Petrila, Zentralblatt MATH, Vol. 1214, 2011)

From the reviews:

"...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

"...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

Spis treści

Introduction*Ordinary Differential Equations*Finite-Difference Approximation of the Wave Equation*Diffusion, Sources and Sinks*Series Expansion Methods*Finite-Volume Methods*Semi-Lagrangian Methods*Physically Insignificant Fast Waves*Nonreflecting Boundary Conditions*Appendix

O autorze

Dale Durran is a professor in the Atmospheric Sciences Department at the University of Washington in Seattle, WA. His research interests include Mesoscale Dynamic, Meteorology, Numerical Methods, Mountain Meteorology, Atmospheric Waves.

Blurb

This book is a major revision of Numerical Methods for Wave Equations in Geophysical Fluid Dynamics; the new title of the second edition conveys its broader scope. The second edition is designed to serve graduate students and researchers studying geophysical fluids, while also providing a non-discipline-specific introduction to numerical methods for the solution of time-dependent differential equations. The methods considered are those at the foundation of real-world atmospheric or ocean models, with the focus being on the essential mathematical properties of each method. The fundamental character of each scheme is examined in prototypical fluid-dynamical problems like tracer transport, chemically reacting flow, shallow-water waves, and waves in an internally stratified fluid. The book includes exercises and is well illustrated with figures linking theoretical analyses to results from actual computations. Changes from the first edition include new chapters, discussions and updates throughout. Dale Durran is Professor and Chair of Atmospheric Sciences and Adjunct Professor of Applied Mathematics at the University of Washington. Reviews from the First Edition: “This book will no doubt become a standard within the atmospheric science community, but its comfortable applied mathematical style will also appeal to many interested in computing advective flows and waves. It is a contemporary and worthy addition to the still-sparse list of quality graduate-level references on the numerical solution of PDEs." SIAM Review, 2000, 42, 755-756 (by David Muraki) “This book presents an extensive overview of past and current numerical methods used in the context of solving wave systems … It is directed primarily at flows that do not develop shocks and focuses on standard fluid problems including tracer transport, the shallow-water equations and the Euler equations … the book is well organized and written and fills a long-standing void for collected material on numerical methods useful for studying geophysical flows." Bulletin of the American Meteorological Society, 2000, 81, 1080-1081 (by Robert Wilhelmson)