462
Index
multistep time-differencing, 56-60
initialization of, 60
Newton polynomial, 308, 331-332
nondispersive wave, 72
nonlinear instability, 159-167
norm
of a grid-point function, 39-40
of a matrix, 109
of a real-valued continuous
function, 174
numerical dispersion, 82
numerical dissipation, 81, 138-139
numerical resolution, 51
numerical smoothing, 82-86
numerical weather prediction, 1
one-way wave equation, 5, 401,
414-418,433
open boundary condition, see
radiation boundary
condition
order of accuracy, 36
of a monotone finite-difference
scheme, 253
orthogonality, 175, 177-178
oscillation equation, 49
pagoda function, 231
partial differential equation
elliptic
approximation by marehing
schemes, 31-32
defined,7-11
hyperbolic
approximation by marehing
schemes, 31-32
defined,4-9,11
and tracer transport, 12
linear, 3
order of, 2
parabolic
defined, 7-11
and tracer transport, 12
Peaceman-Rachford method, 133
Peclet number , 138-139
Petrov-Galerkin method, 216-217
phase speed , 15,72
phase-speed error, 49, 71-72, 91
in finite-difference
approximations to the
2-D advection equation,
120-122
in Hermite-cubic
finite-element
approximations to the
1-0 advection equation,
227-229
in quadratic finite-element
approx imations to the
1-0 advection equation,
222-225
produced by compact
finite-differencing, 87-88
produced by second- and
fourth-order spatial
differencing,73-75
for the semidiscrete 1-0
advection equation,
73-77
on a staggered mesh, 114, 115
physical mode, 57
pole problem , 200-202
positive definite advection schemes,
292-296
antidiffusion via upstream
differencing, 294-296
and ftux-corrected transport,
293,294
potential temperature, 16
Prandtl number, 138
pressure equation
for the anelastic system, 342
for the Boussinesq system,
337,338,340
boundary conditions for,
338-339
for the pseudo-incompressible
system, 342