Tests¶
There is one test located in dclaw/tests/bowl-slosh and described below. Additional not-yet-ready tests are located in dclaw/tests/dev. The applications within this test development directory are not expected to work.
Sloshing water in a parabolic bowl¶
This is a modified version of the bowl-slosh test in geoclaw .
Background¶
Waves in a parabolic bowl with a flat surface sloshing around. An exact analytic solution is known in which the surface stays flat.
In this code, \(x\) and \(y\) are in meters (coordinate_system=1 in setrun.py).
Topography: \(B(x,y) = h_0((x^2 + y^2)/a^2 -1)\),
Depth: \(h(x,y,t) = \max\left(0,~~ (\sigma h_0/a^2)(2x\cos(\omega t) + 2y\sin(\omega t) - \sigma) - B(x,y)\right)\)
Velocities: \(u(x,y,t) = -\sigma \omega \sin(\omega t),\qquad v(x,y,t) = \sigma \omega \cos(\omega t).\)
where \(\omega = \sqrt{2gh_0} / a\).
The period of oscillation is \(T = 2\pi / \omega\).
The following parameters are currently hardwired several places:
\(a = 1, ~~\sigma = 0.5, ~~h = 0.1,~~g = 9.81\)
Instructions¶
This example uses a custom qinit.f90. First recompile the code from within the bowl_slosh directory:
make clean
make clobber
make .exe
Create the topo file before running the code:
make topo
make .data
make .output
make .plots
Alternatively, you may run:
make all
to run all steps. Examine the plots by opening bowl-slosh/_plots/_PlotIndex.html in a browser. We suggest the cross-section movies as the best means for simluation-analytical solution comparison. Finally, we suggest that you also run the equivalent test case in geoclaw (geoclaw/tests/bowl-slosh) and compare the output.
Note
This should be cleaned up: better to put them in a setprob.data file that is read in where needed.
References¶
W. C. Thacker, Some exact solutions to the nonlinear shallow water wave equations, J. Fluid Mech. 107 (1981), 499-508.
J.M. Gallardo, C. Pares, and M. Castro, On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas, J. Comput. Phys. 227(2007) 574-601.
Y. Xing, X. Zhang and C.-W. Shu, Positivity preserving high order well balanced discontinuous Galerkin methods for the shallow water equations , Advances in Water Resources 33 (2010), pp. 1476-1493.
This test problem has been used in several other papers too.