12.1 PASS:
Oscillations in a parabolic container

Author
 Stéphane Popinet
 Command
 sh parabola.sh parabola.gfs
 Version
 1.3.1
 Required files
 parabola.gfs (view) (download)
parabola.sh error.ref
 Running time
 25 seconds
Analytical solutions for the damped oscillations of a liquid in a
parabolic container have been derived by Sampson et al
[40, 25]. Figure 139 illustrates the
numerical and analytical solutions at t = 1500 seconds. Wetting
and drying occur at the two moving contact points and hydrostatic
balance is approached as time passes.
Figure 140 gives the analytical and numerical solutions for the
horizontal component of velocity (which is spatially
constant). Figures 141 and 142 give
the relative errors in surface elevation and horizontal velocity
respectively, as functions of spatial resolution.
The errors are small and largerthanfirstorder convergence rates
are obtained.
See also [33] for details.
Figure 139: Solution at t = 1500 seconds. Six levels of refinement. 
Figure 140: Time evolution of the (spatially constant)
horizontal velocity. Seven levels of refinement. 
Figure 141: Evolution of the relative elevation
error norms as functions of resolution. 
Figure 142: Evolution of the relative velocity error
L2norm as a function of resolution. 
12.1.1 PASS:
Parabolic container with embedded solid

Author
 Hyunuk An, Soonyoung Yu and Stéphane Popinet
 Command
 sh ../parabola.sh solid.gfs
 Version
 120314
 Required files
 solid.gfs (view) (download)
error.ref
 Running time
 4 minutes 6 seconds
Same test case but with a slightlyinclined, narrow channel defined
using embedded solid boundaries.
See also [3] for details.
Figure 143: Time evolution of the (spatially constant)
horizontal velocity. Seven levels of refinement. 
Figure 144: Evolution of the relative elevation
error norms as functions of resolution. 
Figure 145: Evolution of the relative velocity error
L2norm as a function of resolution. 