def analytic_model_fig(ax, var_md, time=1):
lamb = eq.d1_lambda_evol(time)
h_a = eq.d1_height(lamb, var_md["x_range"])
v_a = eq.d1_velocity(lamb, var_md["x_range"])
ax.plot(
var_md["x_range"],
eq.d1_initial(var_md["x_range"]),
"k",
var_md["x_range"],
h_a,
"b",
var_md["x_range"],
var_md["h"],
"r",
)
ax.plot(
var_md["x_range"],
0 * var_md["x_range"],
"k-",
var_md["x_range"],
v_a,
"b--",
var_md["x_range"],
var_md["vx"],
"r--",
)
ps.ticks_changes(ax)
def analytic_model_fig(ax, var_md, time=1):
lamb = eq.d1_lambda_evol(time)
h_a = eq.d1_height(lamb, var_md["x_range"])
v_a = eq.d1_velocity(lamb, var_md["x_range"])
ax.plot(var_md["x_range"], eq.d1_initial(var_md["x_range"]), 'k',
var_md["x_range"], h_a, 'b', var_md["x_range"], var_md["h"], "r")
ax.plot(var_md["x_range"], 0 * var_md["x_range"], "k-", var_md["x_range"],
v_a, 'b--', var_md["x_range"], var_md["vx"], "r--")
ps.ticks_changes(ax)
def analytic_fig(ax, x_lim, time_l=[0,1,2,3], nx=320):
x_range = np.linspace(-x_lim, x_lim, nx)
oznacz = ['k', 'b', 'c', 'y', 'g', 'm', 'r']
for it, time in enumerate(time_l):
lamb = eq.d1_lambda_evol(time)
h = eq.d1_height(lamb, x_range)
v = eq.d1_velocity(lamb, x_range)
ax.plot(x_range, h, oznacz[it])
ax.plot(x_range, v, oznacz[it]+ "--")
ps.ticks_changes(ax)
def analytic_fig(ax, x_lim, time_l=[0, 1, 2, 3], nx=320):
x_range = np.linspace(-x_lim, x_lim, nx)
oznacz = ['k', 'b', 'c', 'y', 'g', 'm', 'r']
for it, time in enumerate(time_l):
lamb = eq.d1_lambda_evol(time)
h = eq.d1_height(lamb, x_range)
v = eq.d1_velocity(lamb, x_range)
ax.plot(x_range, h, oznacz[it])
ax.plot(x_range, v, oznacz[it] + "--")
ps.ticks_changes(ax)
def analytic_model_fig(ax, x_range, h_m, v_m, t_m, it):
lamb = eq.d1_lambda_evol(t_m[it,0])
h_a = eq.d1_height(lamb, x_range)
v_a = eq.d1_velocity(lamb, x_range)
ax.plot(x_range, eq.d1_initial(x_range), 'k', x_range, h_a, 'b',
x_range, h_m[it], "r")
ax.plot(x_range, 0*x_range, "k-", x_range, v_a, 'b--',
x_range, v_m[it], "r--")
ax.set_ylim(-2,2)
ps.ticks_changes(ax)
def analytic_model_fig(ax, x_range, h_m, v_m, t_m, it):
lamb = eq.d1_lambda_evol(t_m[it,0])
h_a = eq.d1_height(lamb, x_range)
v_a = eq.d1_velocity(lamb, x_range)
ax.plot(x_range, eq.d1_initial(x_range), 'k', x_range, h_a, 'b',
x_range, h_m[it], "r")
ax.plot(x_range, 0*x_range, "k--", x_range, v_a, 'b--',
x_range, v_m[it], "r--")
ax.set_ylim(-2,2)
ps.ticks_changes(ax)
def errors(dir, time_l, x_lim):
for it, time in enumerate(time_l):
# reading the model output
var_model = reading_modeloutput(dir, time)
var_model["x_range"] = np.arange(-x_lim + var_model["dx"] / 2., x_lim,
var_model["dx"])
assert (var_model["x_range"].shape == var_model["h"].shape
), "domain size differs from model output shape"
# calculating the analytical solution
lamb = eq.d1_lambda_evol(time)
h_an = eq.d1_height(lamb, var_model["x_range"])
# calculating the errors of the drop depth, eq. 25 and 26 from the paper
h_diff = var_model["h"] - h_an
points_nr = var_model["h"].shape[0]
delh_inf = abs(h_diff).max()
delh_2 = 1. / time * ((h_diff**2).sum() / points_nr)**0.5
# outputing general info
if time == time_l[0]:
file = open(dir + "_stats.txt", "w")
fstring = (
"dx = {dx:.4f}\n"
"dt = {dt:.4f}\n"
"number of points in the domain = {npoints}\n"
"L_inf = max|h_m-h_an|\n"
"L_2 = sqrt(sum(h_m-h_an)^2 / N) / time\n\n"
)
file.write(
fstring.format(dx=var_model["dx"],
dt=var_model["dt"],
npoints=points_nr))
# outputting error statistics
fstring = ("time = {time:.4f}\n"
"max(h_an) = {max_h_an:.8f}\n"
"max(h_num) = {max_h_num:.8f}\n"
"L_inf = {L_inf:.8f}\n"
"L_2 = {L_2:.8f}\n"
"max(px_num) = {max_px_num:.8f}\n\n")
file.write(
fstring.format(time=time,
max_h_an=h_an.max(),
max_h_num=var_model["h"].max(),
L_inf=delh_inf,
L_2=delh_2,
max_px_num=var_model["qx"].max()))
file.close()
def errors(dir, time_l, x_lim):
for it, time in enumerate(time_l):
# reading the model output
var_model = reading_modeloutput(dir, time)
var_model["x_range"] = np.arange(-x_lim+var_model["dx"]/2., x_lim, var_model["dx"])
assert(var_model["x_range"].shape == var_model["h"].shape), "domain size differs from model output shape"
# calculating the analytical solution
lamb = eq.d1_lambda_evol(time)
h_an = eq.d1_height(lamb, var_model["x_range"])
# calculating the errors of the drop depth, eq. 25 and 26 from the paper
h_diff = var_model["h"] - h_an
points_nr = var_model["h"].shape[0]
delh_inf = abs(h_diff).max()
delh_2 = 1./time * ((h_diff**2).sum() / points_nr )**0.5
# outputing general info
if time == time_l[0]:
file = open(dir + "_stats.txt", "w")
fstring = (
"dx = {dx:.4f}\n"
"dt = {dt:.4f}\n"
"number of points in the domain = {npoints}\n"
"L_inf = max|h_m-h_an|\n"
"L_2 = sqrt(sum(h_m-h_an)^2 / N) / time\n\n"
)
file.write(fstring.format(dx = var_model["dx"], dt = var_model["dt"], npoints = points_nr))
# outputting error statistics
fstring = (
"time = {time:.4f}\n"
"max(h_an) = {max_h_an:.8f}\n"
"max(h_num) = {max_h_num:.8f}\n"
"L_inf = {L_inf:.8f}\n"
"L_2 = {L_2:.8f}\n"
"max(px_num) = {max_px_num:.8f}\n\n"
)
file.write(fstring.format(
time = time,
max_h_an = h_an.max(),
max_h_num = var_model["h"].max(),
L_inf = delh_inf,
L_2 = delh_2,
max_px_num = var_model["qx"].max()
)
)
file.close()
