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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 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 [20], Figures 5 and 6.


Figure 156: 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 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.
(a)
(b)
(c)

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 shallow-water 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.
(a) (b)
(c) (d)
(e)


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.
(a)
(b)
(c)
(d)
(e)

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 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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