def main():
x0, x1 = -0.5, 0.5
y0, y1 = -0.5, 0.5
h = .125
nu = 1e3
dt = 0.01
t0 = 0.01
plot_rows, plot_cols = 3, 3
plot_every = 10
x, y = init_position.triangular(x0, x1, y0, y1, cell_size=h)
# initial vorticity and circulation
vort = problems.lamb_oseen.vorticity(x, y, t0, nu=nu)
circ = h**2 * vort
# particle colors
from itertools import cycle, izip as zip
colors = ('#FF0000 #00FF00 #0000FF #FFFF00 #FF00FF #00FFFF '
'#660000 #006600 #000066 #666600 #660066 #006666 '
).split()
colors = [c for (c, _) in zip(cycle(colors), x)]
t = t0
iteration = 0
plot_count = 0
while True:
plot_now = (iteration % plot_every == 0)
if plot_now:
plot_count += 1
pylab.subplot(plot_rows, plot_cols, plot_count,
autoscale_on=False,
xlim=(1.2 * x0, 1.2 * x1),
ylim=(1.2 * y0, 1.2 * y1))
pylab.scatter(x, y, s=2, c=colors, edgecolors='none')
pylab.grid(True)
u, v = vm.eval_velocity(x, y, circ)
#pylab.quiver(x[::10], y[::10], u[::10], v[::10])
if plot_now:
pylab.quiver(x, y, u, v, color=colors)
pylab.title('$t = %.2f$' % t)
# convect
x += u * dt
y += v * dt
iteration += 1
t += dt
if plot_count == plot_rows * plot_cols:
break
pylab.suptitle(ur'Lamb Oseen vortex, $\nu = %.3f$' % nu)
pylab.show()
def euler(x, y, circ, dt, squared_blob_size):
u, v = vm.eval_velocity(x, y, circ=circ,
squared_blob_size=squared_blob_size)
return u, v