458
Index
alternating direction method, 133
amplification factor, 43,49
amplitude error, 49, 71, 72,81
analytic function, 10
anelastic approximation, 21, 25
anelastic equations, 24-25
antidiffusion via upstream
differencing, 294-296
antidiffusive flux, 258
ArakawaJacobian, 166
artificial dissipation, 82-86
Asselin filter, 62-64, 368
backward time-differencing, 50--52,
55,56
barotropic vorticity equation,
163-167
block cyclic reduction, 342
boundary conditions
accuracy of, 408
influence on stability, 409-412
nonlocal , 426, 436
nonreflecting, see radiation
boundary condition, see
wave-absorbing layers,
reflections generated by,
402-408,416-418,
422-423,426-428
well-posed, 397-400
Boussinesq approximation, 20, 23
Boussinesq equations, 23-24, 337
compressible, 351-352, 356,
371
solution via the projection
method , 337-342
Brunt-Väisälä frequency, 18,24
Burgers's equation
conservative differentialdifference
approximations to,
160--163
discontinuous solutions to,
159-160,246-249
finite-element approximations
tO,230--231
generalized, 241
spectral and pseudospectral
approximations to,
193-194
and transonic rarefaction
waves, 274
C grid, 127
Cauchy problem, 409
CFL condition , see
Courant-Fredrichs-Lewy
condition
chapeau function, 213
characteristic curve, 4, 5, 9
and boundary conditions for
I-D hyperbolic equations,
398-402
for Burgers's equation,
and tracer transport, 12
chemically reacting flow,
291-292
collocation, 175, 191
compact differencing, 86-89
for the 2-D advection
equation, 287
phase-speed error of, 87-88
computational mode
of finite-element
approximations to the
I-D advection equation,
222-223,228
ofthe leapfrog scheme, 57-59,
61-64
of the second-order
Adams-Bashforth
scheme, 59-60
of the third-order
Adams-Bashforth
method,70
conjugate gradient method, 342
conservation and stability,
154-157
conservation form
defined,250