Numerical Methods for Wave Equations in Geophysical Fluid DynamicsMathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modem as weIlas the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in AppliedMathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and rein force the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and en courage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the AppliedMathematical Sei ences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface This book is designed to serve as a textbook for graduate students or advanced undergraduates studying numerical methods for the solution of partial differen tial equations goveming wave-like flows. Although the majority of the schemes presented in this text were introduced ineither the applied-rnathematics or atmos pheric-science literature, the focus is not on the nuts-and-bolts details of various atmospheric models but on fundamental numerical methods that have applications in a wide range of scientific and engineering disciplines. |
Contents
1 | |
4 | |
6 | |
8 | |
36 | 17 |
Basic FiniteDifference Methods | 35 |
Problems | 107 |
Problems | 232 |
Problems | 244 |
Physically Insignificant Fast Waves | 336 |
Problems | 436 |
443 | |
457 | |
458 | |
464 | |
Finite Volume Methods | 240 |
Other editions - View all
Numerical Methods for Wave Equations in Geophysical Fluid Dynamics Dale R. Durran Limited preview - 1998 |
Numerical Methods for Wave Equations in Geophysical Fluid Dynamics Dale R. Durran No preview available - 2013 |
Numerical Methods for Fluid Dynamics: With Applications in Geophysics Dale R. Durran No preview available - 2010 |
Common terms and phrases
accuracy Adams-Bashforth advection equation algorithm aliasing error amplification factor amplitude boundary conditions Boussinesq Burgers's equation centered coefficients computational mode conservation law Courant number damping defined difference differencing differential-difference diffusion discrete dispersion relation domain evaluated expansion functions filter finite finite-difference approximation finite-difference scheme finite-element first-order flow flux flux-limited formula Fourier modes Fourier series fourth-order Gaussian quadrature grid points group velocity hyperbolic integration k₁ Lax-Wendroff method leapfrog scheme linear matrix mesh nodes nonlinear numerical approximation numerical solution obtained one-dimensional ordinary differential equations oscillation equation partial differential equations perturbations phase speed phase-speed error physical polynomial preceding problem propagation pseudospectral Runge-Kutta second-order semi-Lagrangian shallow-water shown in Fig simulation spatial derivatives spectral method spherical harmonic third-order time-differencing tion transform trapezoidal true solution truncation error two-dimensional unstable upstream values vertical wave number wavelengths zero Δι ди ду дх Эх