The next basic step is checking convergence of the numerical code to
a certain asymptotic limit, presumably the actual solution of the
equations solved. The grid steps  and  need to
be halved, and the time step  reduced appropriately to
conform with the Courant-Friedrics-Levy (CFL) criterion. The
optimal locations to check convergence are the extreme runup and
rundown. A graph needs to be prepared presenting the variation of
the calculated runup and rundown (ordinate) with the step size
(abscissa). As the step size is reduced, the numerical predictions
should be seen to converge to a certain value, and further
reductions in step size should not change the results.
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