13.1 PASS:
Circular dam break on a sphere

Author
 Stéphane Popinet
 Command
 gerris2D m lonlat.gfs
 Version
 090924
 Required files
 lonlat.gfs (view) (download)
isolines.gfv
 Running time
 3 minutes 2 seconds
An initial circular cylinder collapses and creates shock and
rarefaction waves. The initial condition are radiallysymmetric and
should remain so. The problem is discretised using
longitudelatitude spherical coordinates. Deviations from radial
symmetry are a measure of the accuracy of treatment of geometric
source terms.
This test case was proposed by [20], Figures 5 and 6.
Figure 156: Solution to the shallowwater equations computed on a
longitudelatitude grid in the domain
[−75^{∘},75^{∘}]×[−75^{∘},75^{∘}] with 256×
256 points. The solution is shown at times (a) t=0.3, (b)
t=0.6, and (c) t=0.9. The contours do not appear circular
because the solution has been projected down to a plane. 
Figure 157: Scatter plot of the (radial) solution shown in Figure
156. The green line is the average solution. The solution
is shown at times (a) t=0.3, (b) t=0.6, and (c) t=0.9. 
13.1.1 PASS:
Circular dam break on a “cubed sphere”

Author
 Stéphane Popinet
 Command
 gerris2D m cubed.gfs
 Version
 120812
 Required files
 cubed.gfs (view) (download)
isolines.gfv
 Running time
 8 minutes 24 seconds
Same test case but using a “cubed sphere” metric and adaptive mesh
refinement. There is noticeable distortion close to the cubed sphere
“poles” (Figures 158.(c) and 159.(c)).
Figure 158: Solution to the shallowwater equations
computed on a “cubed sphere” with adaptive mesh refinement.
The solution is shown at times (a) t=0.3, (b)
t=0.6, (c) t=0.9, (d) t=1.2, and (e) t=1.5. The contours do
not appear circular because the solution has been projected down to
a plane. 
Figure 159: Scatter plot of the (radial) solution shown in Figure
158. The green line is the average solution. The solution
is shown at times (a) t=0.3, (b) t=0.6, (c) t=0.9, (d)
t=1.2, and (e) t=1.5. 
13.1.2 PASS:
Circular dam break on a rotating sphere

Author
 Stéphane Popinet
 Command
 gerris2D m coriolis.gfs
 Version
 090924
 Required files
 coriolis.gfs (view) (download)
isolines.gfv
 Running time
 5 minutes 56 seconds
Similar test case but with rotation. See also test case of [20], Figure 7.
Figure 160: Solution to the rotating shallowwater equations computed
on a longitudelatitude grid in the domain
[−75^{∘},75^{∘}]×[−75^{∘},75^{∘}] with 256×
256 points. The Coriolis parameter is set to f=10. The solution
is shown at times (a) t=0.4, (b) t=0.8, and (c) t=1.2. 