460
Index
Eulerian form , 303
Eulerian-Lagrangian methods, see
serni-Lagrangian methods
Exner function, 17
explicit time-differencing, 53
fast Fourier transform (FFf), 180,
235
efficiency of, 185-186
filtered equations, 11, 20-26
finite difference, 36
on an irregular mesh, 101
finite Fourier transfonn, 179-180
finite-difference method, 26-27
finite-difference operator notation,
439-440
finite-element method, 29
comparison with compact
differencing, 215, 232
in two dimensions, 231-234
using the Galerkin
approximation
with cubic expansion
functions, 226-231
with linear expansion
functions, 214-216
with quadratic expansion
functions, 219-225
using the Petrov-Galerkin
approximation, 216-217
using the Taylor-Galerkin
approximation, 217-219
using triangular elements,
232-234
finite-volume method, 27-28
defined,250
Fjertoft's theorem, 164-165
flux form, 157,241-243,297
flux-corrected transport (FeT),
257-263,269-271
in two dimensions, 277 , 278
iterative flux correction, 263
and positive definite advection,
293-294
the Zalesak corrector, 260-262
flux-limiter methods, 263-272
for 2-D flow, 279-290
in curvilinear coordinates,
296-297
forward time-differencing, 50-52,
55 ,56
stability of, 51, 90
forward-backward
time-differencing, 54
forward-backward approximation
to the shaIIow-water
equations, 115, 117,200,
360
Fourier series , 177
and poor resolution, 178-179
fractional-step methods, 129-136
for scalar conservation laws,
277
stability of, 134-136
time splitting, 359-372
truncation error of, 130-133
frequency, 72
frozen-coefficient stability analysis,
147,169
Galerkin approximation
con servation properties of,
189-190
defined,I75
equivalence to minimizing the
e2-nonn of the residual,
175-176
and the finite-elernent-method,
213
Gaussian quadrature, 203-207
Godunov's method, 272-274
Godunov-Ryabenki condition,
409
gravity waves, 11 ,335-336,347,
352-356,390-391
dispersion relation, 19
group velocity, 72
for the semidiscrete I-D
advection equation,