A simulation is initialised with an exact solution found by Lamb [23] for inertia-gravity waves in a circular, flat-bottomed basin on an f-plane.
The waves should rotate unchanged around the basin. This is a good test of the shallow-water solver with Coriolis terms and non-trivial coastlines.
Figure 135 illustrates the solution obtained after three wave periods.
Following [11], Table 13 presents the phase error and the maximum correlation between the computed solution and the exact solution. Note that these results are not directly comparable to [11], because the timestep used is much larger. The time-explicit codes tested in [11] have stronger stability requirements than Gerris.
Level Maximum C Angle of max C 5 0.9253 2.4 6 1 0.1 7 1 0
Same test case as before but with adaptive refinement (using the vorticity criterion).
Figure 136 illustrates the solution obtained after three wave periods.
Level Maximum C Angle of max C 5 0.9221 2.6 6 0.9981 0.7 7 0.9985 0.3