302
5. Finite-Volume Methods
plot the log of the error versus the log of Sx to estimate the power of !1x
that is proportional to the error as Sx --7 O. Compare these results to the
theoretical order of accuracy for the standard upstream and Lax-Wendroff
methods.
16. *Compare simulations of the geostrophic adjustment problem described in
Problem 12 of Chapter 3 obtained using a flux-limiter scheme with the
MC limiter and flux-corrected transport. Consider both the initial conditions: the discontinuous step and the slightly smoothed step. In order to
use the constant-wind-speed advection algorithms presented in this chapter,
transform the goveming equations to an equivalent system for the unknown
functions u+ gn]c, u - snt». and v (where c
2 = gH). Use upstream differencing and the Lax-Wendroff scheme for the monotone and second-order
methods. Treat the Coriolis terms in the transformed system via operator
splitting.