Numerical Methods for Fluid Dynamics: With Applications to Geophysics [Paperback]

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

The new title of this major revision of Numerical Methods for Wave Equations in Geophysical Fluid Dynamics conveys its broader scope. Aimed at those studying geophysical fluids, it also helps find numerical solutions to time-dependent differential equations.

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

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 f?r Mathematik, Vol. 166 (1), April, 2012)

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