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12.1  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
2 minutes 44 seconds

An initial circular cylinder collapses and creates shock and rarefaction waves. The initial condition are radially-symmetric and should remain so. The problem is discretised using longitude-latitude spherical coordinates. Deviations from radial symmetry are a measure of the accuracy of treatment of geometric source terms.

This test case was proposed by [13], Figures 5 and 6.


Figure 103: Solution to the shallow-water equations computed on a longitude-latitude 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.
(a) (b)
(c)


Figure 104: Scatter plot of the (radial) solution shown in Figure 103. 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.
(a)
(b)
(c)

12.1.1  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
4 minutes 39 seconds

Similar test case but with rotation. See also test case of [13], Figure 7.


Figure 105: Solution to the rotating shallow-water equations computed on a longitude-latitude 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.
(a) (b)
(c)


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