Advection (conservative form)

Scalar advection problem in conservative form with variable velocity field. There are four Riemann solvers that can be tried out here, all described in LeVeque (Cambridge Press, 2002)

rp-solver=1 : Q-star approach in which a $q^*$ value is defined to enforce flux continuity across the stationery wave.
rp-solver=2 : Wave-decomposition approach based on solving the Riemann problem for system of two equations.
rp-solver=3 : Edge centered velocities are used to construct classic update based on flux formulation
rp=sovler=4 : F-wave approach.

Two examples are avaible. In Example 1, the velocity field $u(x)$ is positive. In Example 2, the velocity field changes sign. Both velocity fields have non-zero divergence.

Run code in serial mode (will work, even if code is compiled with MPI)



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!swirlcons --user:example=2 --user:rp-solver=4

Or, run code in parallel mode (command may need to be customized, depending your on MPI installation.)



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#!mpirun -n 4 swirlcons

Create PNG files for web-browser viewing, or animation.



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%run make_plots.py

View PNG files in browser, using URL above, or create an animation of all PNG files, using code below.



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%pylab inline



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import glob
from matplotlib import image
from clawpack.visclaw.JSAnimation import IPython_display
from matplotlib import animation

figno = 0
fname = '_plots/*fig' + str(figno) + '.png'
filenames=sorted(glob.glob(fname))

fig = plt.figure()
im = plt.imshow(image.imread(filenames[0]))
def init():
    im.set_data(image.imread(filenames[0]))
    return im,

def animate(i):
    image_i=image.imread(filenames[i])
    im.set_data(image_i)
    return im,

animation.FuncAnimation(fig, animate, init_func=init,
                              frames=len(filenames), interval=500, blit=True)