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#!/usr/bin/env python | ||
# encoding: utf-8 | ||
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r""" | ||
Shallow water flow | ||
================== | ||
Solve the one-dimensional shallow water equations including bathymetry: | ||
.. math:: | ||
h_t + (hu)_x & = 0 \\ | ||
(hu)_t + (hu^2 + \frac{1}{2}gh^2)_x & = -g h b_x. | ||
Here h is the depth, u is the velocity, g is the gravitational constant, and b | ||
the bathymetry. | ||
""" | ||
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import numpy | ||
from clawpack import riemann | ||
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def setup(use_petsc=False, outdir='./_output', solver_type='classic'): | ||
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if use_petsc: | ||
import clawpack.petclaw as pyclaw | ||
else: | ||
from clawpack import pyclaw | ||
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solver = pyclaw.ClawSolver1D(riemann.shallow_1D_py.shallow_fwave_1d) | ||
solver.limiters = pyclaw.limiters.tvd.vanleer | ||
solver.kernel_language = "Python" | ||
solver.fwave = True | ||
solver.num_waves = 2 | ||
solver.num_eqn = 2 | ||
solver.bc_lower[0] = pyclaw.BC.extrap | ||
solver.bc_upper[0] = pyclaw.BC.extrap | ||
solver.aux_bc_lower[0] = pyclaw.BC.extrap | ||
solver.aux_bc_upper[0] = pyclaw.BC.extrap | ||
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xlower = -1.0 | ||
xupper = 1.0 | ||
x = pyclaw.Dimension('x', xlower, xupper, 500) | ||
domain = pyclaw.Domain(x) | ||
state = pyclaw.State(domain, 2, 1) | ||
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# Gravitational constant | ||
state.problem_data['grav'] = 9.8 | ||
state.problem_data['sea_level'] = 0.0 | ||
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xc = state.grid.x.centers | ||
state.aux[0, :] = 0.8 * numpy.exp(-xc**2 / 0.2**2) - 1.0 | ||
state.q[0, :] = 0.1 * numpy.exp(-(xc + 0.4)**2 / 0.2**2) - state.aux[0, :] | ||
state.q[1, :] = 0.0 | ||
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claw = pyclaw.Controller() | ||
claw.keep_copy = True | ||
claw.tfinal = 1.0 | ||
claw.solution = pyclaw.Solution(state, domain) | ||
claw.solver = solver | ||
claw.outdir = outdir | ||
claw.setplot = setplot | ||
claw.write_aux_init = True | ||
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return claw | ||
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#-------------------------- | ||
def setplot(plotdata): | ||
#-------------------------- | ||
""" | ||
Specify what is to be plotted at each frame. | ||
Input: plotdata, an instance of visclaw.data.ClawPlotData. | ||
Output: a modified version of plotdata. | ||
""" | ||
plotdata.clearfigures() # clear any old figures,axes,items data | ||
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# Plot variables | ||
def bathy(current_data): | ||
return current_data.aux[0, :] | ||
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def eta(current_data): | ||
return current_data.q[0, :] + bathy(current_data) | ||
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def velocity(current_data): | ||
return current_data.q[1, :] / current_data.q[0, :] | ||
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rgb_converter = lambda triple: [float(rgb) / 255.0 for rgb in triple] | ||
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# Figure for depth | ||
plotfigure = plotdata.new_plotfigure(name='Depth', figno=0) | ||
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# Axes for water depth | ||
plotaxes = plotfigure.new_plotaxes() | ||
plotaxes.xlimits = [-1.0, 1.0] | ||
plotaxes.ylimits = [-1.1, 0.2] | ||
plotaxes.title = 'Water Depth' | ||
plotaxes.axescmd = 'subplot(211)' | ||
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plotitem = plotaxes.new_plotitem(plot_type='1d_fill_between') | ||
plotitem.plot_var = eta | ||
plotitem.plot_var2 = bathy | ||
plotitem.color = rgb_converter((67,183,219)) | ||
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plotitem = plotaxes.new_plotitem(plot_type='1d_plot') | ||
plotitem.plot_var = bathy | ||
plotitem.color = 'k' | ||
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plotitem = plotaxes.new_plotitem(plot_type='1d_plot') | ||
plotitem.plot_var = eta | ||
plotitem.color = 'k' | ||
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# Axes for velocity | ||
plotaxes = plotfigure.new_plotaxes() | ||
plotaxes.axescmd = 'subplot(212)' | ||
plotaxes.xlimits = [-1.0, 1.0] | ||
plotaxes.ylimits = [-0.5, 0.5] | ||
plotaxes.title = 'Velocity' | ||
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plotitem = plotaxes.new_plotitem(plot_type='1d_plot') | ||
plotitem.plot_var = velocity | ||
plotitem.color = 'b' | ||
plotitem.kwargs = {'linewidth':3} | ||
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return plotdata | ||
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if __name__=="__main__": | ||
from clawpack.pyclaw.util import run_app_from_main | ||
output = run_app_from_main(setup,setplot) |