README.html Source file:   README.txt Directory:   /Users/rjl/git/rjleveque/clawpack-4.6.3/apps/tsunami/bowl-slosh Converted:   Mon Jan 21 2013 at 20:15:27   using clawcode2html This documentation file will not reflect any later changes in the source file.

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## GeoClaw Sample Code

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 (iccordsys=1 in setrun.py [.html]).

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:

$a = 1, ~~\sigma = 0.5, ~~h = 0.1,~~g = 9.81$

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 , submitted to Advances in Water Resources. preprint

This test problem has been used in several other papers too.

To run the code, see Instructions

#### Plots of results

After running this code and creating plots via "make .plots", you should be able to view the plots in _plots/_PlotIndex.html .

#### Fortran files

Makefile [.html]
Determines which version of fortran files are used when compiling the code with make and specifies where output and plots should be directed. Type "make .help" at the Unix prompt for options.

#### Python files

maketopo.py [.html]
Used to create topo file and qinit data file.

setrun.py [.html]
This file contains a function that specifies what run-time parameters will be used.

setplot.py [.html]
This file contains a function that specifies what plots will be done and sets various plotting parameters.

#### Data files

The .data files are automatically generated using the information in setrun.py [.html].

#### Instructions

To make topo and qinit data files:

  $make topo  To make all data files, edit setrun.py and then $ make .data


To run code:

You may need to type

  $make new  to make sure the modules are accessible. Then run the code with $ make .output


To plot results, either generate html pages via:

  $make .plots  or view interactively using ipython and Iplotclaw. All of this can be done with: $ source make_all.py