def main(dir,
casename="fct+iga",
lamb_x0=2.,
lamb_y0=1.,
time_l=[1, 3, 7],
dt=0.01,
nxy=400,
xy_lim=10,
eps=1.e-7):
plt.figure(1, figsize=(9, 8))
#plotting comparison between analytic solution and model results
for it, time in enumerate(time_l):
print "plotting for " + casename + ", t = " + str(time)
#model variables TODO: time
h_m, px_m, py_m = reading_modeloutput(dir +
"spreading_drop_2delipsa_" +
casename +
".out/timestep0000000" +
str(int(time / dt)) + '.h5')
# calculate velocity (momentum/height) only in the droplet region.
vy_m = np.where(h_m > eps, py_m / h_m, 0)
vx_m = np.where(h_m > eps, px_m / h_m, 0)
# calculating the analatycial solution for t=time
x_range = y_range = np.linspace(-xy_lim, xy_lim, nxy)
lamb_ar = an_eq.d2_el_lamb_lamb_t_evol(time, lamb_x0, lamb_y0)
h_an = an_eq.d2_el_height_plane(lamb_ar[0], lamb_ar[2], x_range,
y_range)
v_an = an_eq.d2_el_velocity_tot_plane(lamb_ar[0], lamb_ar[1],
lamb_ar[2], lamb_ar[3], x_range,
y_range)
# calculating depth for t=0
h_an0 = an_eq.d2_el_height_plane(2, 1, x_range, x_range)
# two vertical cross-scections
hx_an, hy_an = h_an[nxy / 2, :], h_an[:, nxy / 2]
hx_an0, hy_an0 = h_an0[nxy / 2, :], h_an0[:, nxy / 2]
vx_an = np.where(hx_an > eps, x_range / lamb_ar[0] * lamb_ar[1], 0)
vy_an = np.where(hy_an > eps, y_range / lamb_ar[2] * lamb_ar[3], 0)
#plotting xz vertical cross-sections
ax = plt.subplot(len(time_l), 2, 2 * it + 1)
lab_op = ["u"]
if it == len(time_l) - 1:
lab_op = lab_op + ["x"]
analytic_model_fig(ax, np.linspace(-xy_lim, xy_lim, nxy),
np.zeros(nxy), h_m[:, nxy / 2], vx_m[:, nxy / 2],
hx_an0, hx_an, vx_an, lab_op, " t= " + str(time))
#plotting yz vertical cross-sections
ax = plt.subplot(len(time_l), 2, 2 * it + 2)
lab_op = ["v"]
if it == len(time_l) - 1:
lab_op = lab_op + ["y"]
analytic_model_fig(ax, np.linspace(-xy_lim, xy_lim, nxy),
np.zeros(nxy), h_m[nxy / 2, :], vy_m[nxy / 2, :],
hy_an0, hy_an, vy_an, lab_op, " t= " + str(time))
plt.savefig("fig6.pdf")
plt.show()
def main(dir, casename="fct+iga", lamb_x0=2., lamb_y0=1., time_l=[1,3,7],
dt=0.01, nxy=400, xy_lim=10, eps=1.e-7):
plt.figure(1, figsize = (9,8))
#plotting comparison between analytic solution and model results
for it, time in enumerate(time_l):
print "plotting for " + casename + ", t = " + str(time)
#model variables TODO: time
h_m, px_m, py_m = reading_modeloutput(dir+"spreading_drop_2delipsa_" + casename + ".out/timestep0000000" + str(int(time/dt)) + '.h5')
# calculate velocity (momentum/height) only in the droplet region.
vy_m = np.where(h_m>eps, py_m / h_m, 0)
vx_m = np.where(h_m>eps, px_m / h_m, 0)
# calculating the analatycial solution for t=time
x_range = y_range = np.linspace(-xy_lim, xy_lim, nxy)
lamb_ar = an_eq.d2_el_lamb_lamb_t_evol(time, lamb_x0, lamb_y0)
h_an = an_eq.d2_el_height_plane(lamb_ar[0], lamb_ar[2], x_range, y_range)
v_an = an_eq.d2_el_velocity_tot_plane(lamb_ar[0], lamb_ar[1], lamb_ar[2],
lamb_ar[3], x_range, y_range)
# calculating depth for t=0
h_an0 = an_eq.d2_el_height_plane(2, 1, x_range, x_range)
# two vertical cross-scections
hx_an, hy_an = h_an[nxy/2,:], h_an[:,nxy/2]
hx_an0, hy_an0 = h_an0[nxy/2,:], h_an0[:,nxy/2]
vx_an = np.where(hx_an>eps, x_range/lamb_ar[0] * lamb_ar[1],0)
vy_an = np.where(hy_an>eps, y_range/lamb_ar[2] * lamb_ar[3], 0)
#plotting xz vertical cross-sections
ax = plt.subplot(len(time_l),2,2*it+1)
lab_op = ["u"]
if it == len(time_l)-1:
lab_op = lab_op + ["x"]
analytic_model_fig(ax,
np.linspace(-xy_lim, xy_lim, nxy),np.zeros(nxy),
h_m[:,nxy/2], vx_m[:, nxy/2], hx_an0, hx_an, vx_an,
lab_op, " t= "+str(time))
#plotting yz vertical cross-sections
ax = plt.subplot(len(time_l),2,2*it+2)
lab_op = ["v"]
if it == len(time_l)-1:
lab_op = lab_op + ["y"]
analytic_model_fig(ax,
np.linspace(-xy_lim, xy_lim, nxy), np.zeros(nxy),
h_m[nxy/2,:], vy_m[nxy/2,:], hy_an0, hy_an, vy_an,
lab_op, " t= "+str(time))
plt.savefig("fig6.pdf")
plt.show()
def main(dir,
lamb_x0=2.,
lamb_y0=1.,
time=7,
dt=0.01,
dx=0.05,
xy_lim=10,
casename="fct+iga",
eps=1.e-7):
x_range = y_range = np.arange(-xy_lim, xy_lim, dx)
time_str = str(int(time / dt))
h_m, px_m, py_m = reading_modeloutput(dir + "spreading_drop_2delipsa_" +
casename + ".out/timestep0000000" +
time_str + '.h5')
#calculating the analytical solution
lamb_ar = an_eq.d2_el_lamb_lamb_t_evol(time, lamb_x0, lamb_y0)
h_an = an_eq.d2_el_height_plane(lamb_ar[0], lamb_ar[2], x_range, y_range)
#the error is normalized by initial height of the drop
h0_max = 1. / (lamb_x0 * lamb_y0)
h_diff = abs(h_m - h_an) / h0_max
print "max of abs(h_m-h_an), h_an.max, h_m.max", abs(
h_diff).max(), h_an.max(), h_m.max()
levels_diff = np.linspace(1.e-10, 2.e-3, 4)
plt.figure(1, figsize=(3., 3.))
ax = plt.subplot(1, 1, 1, aspect='equal')
contour_plot(ax, h_diff, x_range, y_range, levels_var=levels_diff)
plt.savefig("fig7.pdf")
plt.show()
def errors(dir, dt, dx, time_l, xy_lim, casename, eps, lamb_x0=2., lamb_y0=1.):
x_range = y_range = np.arange(-xy_lim, xy_lim, dx)
for it, time in enumerate(time_l):
print "\n", "TIME t = " + str(time), "dx, dt", dx, dt
time_str = str(int(time/dt))
# reading the mode output
# TODO: simplify the files names
if time/dt >= 1000:
h_m, px_m, py_m = reading_modeloutput(dir + casename + ".out/timestep000000" + time_str + '.h5')
elif time/dt < 100:
h_m, px_m, py_m = reading_modeloutput(dir + casename + ".out/timestep00000000" + time_str + '.h5')
else:
h_m, px_m, py_m = reading_modeloutput(dir + casename + ".out/timestep0000000" + time_str + '.h5')
# calculating the analytical solution
lamb_ar = an_eq.d2_el_lamb_lamb_t_evol(time, lamb_x0=lamb_x0, lamb_y0=lamb_y0)
h_an = an_eq.d2_el_height_plane(lamb_ar[0], lamb_ar[2], x_range, y_range)
# calculating the errors of the drop depth, eq. 25 and 26 from the paper
h_diff = h_m - h_an
points_nr = h_m.shape[0]*h_m.shape[1]
print "number of points in the domain, max(h_an), max(h_num)", points_nr, h_an.max(), h_m.max()
h0_max = 1. / lamb_x0 / lamb_y0
delh_inf = abs(h_diff).max() / h0_max
delh_2 = 1./time * ((h_diff**2).sum() / points_nr )**0.5
print "L_inf = max|h_m-h_an|/h_0", delh_inf
print "L_2 = sqrt(sum(h_m-h_an)^2 / N) / time", delh_2, "\n"
def main(dir, lamb_x0=2.0, lamb_y0=1.0, time=7, dt=0.01, dx=0.05, xy_lim=10, casename="fct+iga", eps=1.0e-7):
x_range = y_range = np.arange(-xy_lim, xy_lim, dx)
time_str = str(int(time / dt))
h_m, px_m, py_m = reading_modeloutput(
dir + "spreading_drop_2delipsa_" + casename + ".out/timestep0000000" + time_str + ".h5"
)
# calculating the analytical solution
lamb_ar = an_eq.d2_el_lamb_lamb_t_evol(time, lamb_x0, lamb_y0)
h_an = an_eq.d2_el_height_plane(lamb_ar[0], lamb_ar[2], x_range, y_range)
# the error is normalized by initial height of the drop
h0_max = 1.0 / (lamb_x0 * lamb_y0)
h_diff = abs(h_m - h_an) / h0_max
print "max of abs(h_m-h_an), h_an.max, h_m.max", abs(h_diff).max(), h_an.max(), h_m.max()
levels_diff = np.linspace(1.0e-10, 2.0e-3, 4)
plt.figure(1, figsize=(3.0, 3.0))
ax = plt.subplot(1, 1, 1, aspect="equal")
contour_plot(ax, h_diff, x_range, y_range, levels_var=levels_diff)
plt.savefig("fig7.pdf")
plt.show()
def errors(dir, dt, dx, time_l, xy_lim, casename, eps, lamb_x0=2., lamb_y0=1.):
x_range = y_range = np.arange(-xy_lim, xy_lim, dx)
for it, time in enumerate(time_l):
print "\n", "TIME t = " + str(time), "dx, dt", dx, dt
time_str = str(int(time / dt))
# reading the mode output
# TODO: simplify the files names
if time / dt >= 1000:
h_m, px_m, py_m = reading_modeloutput(dir + casename +
".out/timestep000000" +
time_str + '.h5')
elif time / dt < 100:
h_m, px_m, py_m = reading_modeloutput(dir + casename +
".out/timestep00000000" +
time_str + '.h5')
else:
h_m, px_m, py_m = reading_modeloutput(dir + casename +
".out/timestep0000000" +
time_str + '.h5')
# calculating the analytical solution
lamb_ar = an_eq.d2_el_lamb_lamb_t_evol(time,
lamb_x0=lamb_x0,
lamb_y0=lamb_y0)
h_an = an_eq.d2_el_height_plane(lamb_ar[0], lamb_ar[2], x_range,
y_range)
# calculating the errors of the drop depth, eq. 25 and 26 from the paper
h_diff = h_m - h_an
points_nr = h_m.shape[0] * h_m.shape[1]
print "number of points in the domain, max(h_an), max(h_num)", points_nr, h_an.max(
), h_m.max()
h0_max = 1. / lamb_x0 / lamb_y0
delh_inf = abs(h_diff).max() / h0_max
delh_2 = 1. / time * ((h_diff**2).sum() / points_nr)**0.5
print "L_inf = max|h_m-h_an|/h_0", delh_inf
print "L_2 = sqrt(sum(h_m-h_an)^2 / N) / time", delh_2, "\n"