conservation law, 157,243-244
consistency
of a finite-difference method,
39
of numerically approximated
fluxes to a conservation
law, 250
convergence, 40-41
to the entropy consistent weak
solution, 251
to a false solution, 241-243
to a weak solution, 250
convolution sum, 186
Courant-Fredrichs-Lewy
condition, 45-47, 306
Crank-Nicolson method, 137
CTU method, 123-125,280-282
and semi-Lagrangian schemes,
309
curvilinear coordinates,
296-297
decelerating time difference, 49
diffusion equation , 136-138
dispersion relation
for differential-difference
approximations to the
I-D advection equation,
73-77,79
exact for
the I-D advection equation,
72
the 2-D advection equation,
120
the middle-latitude ß-plane
equations, 390
for finite-difference
approximations to
the I-D advection equation ,
91-94
the I-D shallow-water
equations, 112-113, 117
the 2-D advection equation,
117-120
Index
459
the Boussinesq equations,
126-128
for hydrostatic gravity waves,
374
for leapfrog approximations to
the compressible
Boussinesq equations,
352-353
for linear finite-element
approximations to the
I-D advection equation,
215
for numerical approximations
to the 2-D shallow-water
equations of the sphere,
201
for semi-implicit
approximations to
the I-D shallow-water
equations ,348-349
the compressible
Boussinesq equations,
354-356
divergence damper, 369-370
domain of dependence, 45
domain of influence, 45
donor cell method, see upstream
differencing
Dufort-Frankel method, 102
eddy diffusivity, 13, 139, 167
energy method, 41-42, 154-158
entropy condition , 246-249
Euler equations, 337
approximation via leapfrog
time differencing ,
352-353
approximation via the
semi-implicit method,
353-359
hyperbolic nature of,
16-19
simplified, 350-352
Euler's method, see forward
time-differencing