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Commit b0aee79f authored by Josh Borrow's avatar Josh Borrow
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Added improved plotting for the Gresho Vortex

parent e4128a10
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examples/HydroTests/GreshoVortex_2D/plotSolution.py
View file @ b0aee79f
###############################################################################
# This file is part of SWIFT.
# Copyright (c) 2016 Matthieu Schaller (matthieu.schaller@durham.ac.uk)
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
# This file is part of SWIFT.
# Copyright (c) 2016 Matthieu Schaller (matthieu.schaller@durham.ac.uk)
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
##############################################################################
# Computes the analytical solution of the Gresho-Chan vortex and plots the SPH answer
# Parameters
gas_gamma = 5./3. # Gas adiabatic index
rho0 = 1 # Gas density
P0 = 0. # Constant additional pressure (should have no impact on the dynamics)
gas_gamma = 5.0 / 3.0 # Gas adiabatic index
rho0 = 1 # Gas density
P0 = 0.0 # Constant additional pressure (should have no impact on the dynamics)
# ---------------------------------------------------------------
# Don't touch anything after this.
# ---------------------------------------------------------------
import matplotlib
matplotlib.use("Agg")
from pylab import *
from scipy import stats
import h5py
# Plot parameters
params = {'axes.labelsize': 10,
'axes.titlesize': 10,
'font.size': 12,
'legend.fontsize': 12,
'xtick.labelsize': 10,
'ytick.labelsize': 10,
'text.usetex': True,
'figure.figsize' : (9.90,6.45),
'figure.subplot.left' : 0.045,
'figure.subplot.right' : 0.99,
'figure.subplot.bottom' : 0.05,
'figure.subplot.top' : 0.99,
'figure.subplot.wspace' : 0.15,
'figure.subplot.hspace' : 0.12,
'lines.markersize' : 6,
'lines.linewidth' : 3.,
'text.latex.unicode': True
}
rcParams.update(params)
rc('font',**{'family':'sans-serif','sans-serif':['Times']})
style.use("../../../tools/stylesheets/mnras.mplstyle")
snap = int(sys.argv[1])
......@@ -69,21 +49,27 @@ solution_v_r = zeros(N)
for i in range(N):
if solution_r[i] < 0.2:
solution_P[i] = P0 + 5. + 12.5*solution_r[i]**2
solution_v_phi[i] = 5.*solution_r[i]
solution_P[i] = P0 + 5.0 + 12.5 * solution_r[i] ** 2
solution_v_phi[i] = 5.0 * solution_r[i]
elif solution_r[i] < 0.4:
solution_P[i] = P0 + 9. + 12.5*solution_r[i]**2 - 20.*solution_r[i] + 4.*log(solution_r[i]/0.2)
solution_v_phi[i] = 2. -5.*solution_r[i]
solution_P[i] = (
P0
+ 9.0
+ 12.5 * solution_r[i] ** 2
- 20.0 * solution_r[i]
+ 4.0 * log(solution_r[i] / 0.2)
)
solution_v_phi[i] = 2.0 - 5.0 * solution_r[i]
else:
solution_P[i] = P0 + 3. + 4.*log(2.)
solution_v_phi[i] = 0.
solution_P[i] = P0 + 3.0 + 4.0 * log(2.0)
solution_v_phi[i] = 0.0
solution_rho = ones(N) * rho0
solution_s = solution_P / solution_rho**gas_gamma
solution_u = solution_P /((gas_gamma - 1.)*solution_rho)
solution_s = solution_P / solution_rho ** gas_gamma
solution_u = solution_P / ((gas_gamma - 1.0) * solution_rho)
# Read the simulation data
sim = h5py.File("gresho_%04d.hdf5"%snap, "r")
sim = h5py.File("gresho_%04d.hdf5" % snap, "r")
boxSize = sim["/Header"].attrs["BoxSize"][0]
time = sim["/Header"].attrs["Time"][0]
scheme = sim["/HydroScheme"].attrs["Scheme"]
......@@ -92,133 +78,153 @@ neighbours = sim["/HydroScheme"].attrs["Kernel target N_ngb"]
eta = sim["/HydroScheme"].attrs["Kernel eta"]
git = sim["Code"].attrs["Git Revision"]
pos = sim["/PartType0/Coordinates"][:,:]
x = pos[:,0] - boxSize / 2
y = pos[:,1] - boxSize / 2
vel = sim["/PartType0/Velocities"][:,:]
r = sqrt(x**2 + y**2)
v_r = (x * vel[:,0] + y * vel[:,1]) / r
v_phi = (-y * vel[:,0] + x * vel[:,1]) / r
v_norm = sqrt(vel[:,0]**2 + vel[:,1]**2)
pos = sim["/PartType0/Coordinates"][:, :]
x = pos[:, 0] - boxSize / 2
y = pos[:, 1] - boxSize / 2
vel = sim["/PartType0/Velocities"][:, :]
r = sqrt(x ** 2 + y ** 2)
v_r = (x * vel[:, 0] + y * vel[:, 1]) / r
v_phi = (-y * vel[:, 0] + x * vel[:, 1]) / r
v_norm = sqrt(vel[:, 0] ** 2 + vel[:, 1] ** 2)
rho = sim["/PartType0/Densities"][:]
u = sim["/PartType0/InternalEnergies"][:]
S = sim["/PartType0/Entropies"][:]
P = sim["/PartType0/Pressures"][:]
# Bin te data
r_bin_edge = np.arange(0., 1., 0.02)
r_bin = 0.5*(r_bin_edge[1:] + r_bin_edge[:-1])
rho_bin,_,_ = stats.binned_statistic(r, rho, statistic='mean', bins=r_bin_edge)
v_bin,_,_ = stats.binned_statistic(r, v_phi, statistic='mean', bins=r_bin_edge)
P_bin,_,_ = stats.binned_statistic(r, P, statistic='mean', bins=r_bin_edge)
S_bin,_,_ = stats.binned_statistic(r, S, statistic='mean', bins=r_bin_edge)
u_bin,_,_ = stats.binned_statistic(r, u, statistic='mean', bins=r_bin_edge)
rho2_bin,_,_ = stats.binned_statistic(r, rho**2, statistic='mean', bins=r_bin_edge)
v2_bin,_,_ = stats.binned_statistic(r, v_phi**2, statistic='mean', bins=r_bin_edge)
P2_bin,_,_ = stats.binned_statistic(r, P**2, statistic='mean', bins=r_bin_edge)
S2_bin,_,_ = stats.binned_statistic(r, S**2, statistic='mean', bins=r_bin_edge)
u2_bin,_,_ = stats.binned_statistic(r, u**2, statistic='mean', bins=r_bin_edge)
rho_sigma_bin = np.sqrt(rho2_bin - rho_bin**2)
v_sigma_bin = np.sqrt(v2_bin - v_bin**2)
P_sigma_bin = np.sqrt(P2_bin - P_bin**2)
S_sigma_bin = np.sqrt(S2_bin - S_bin**2)
u_sigma_bin = np.sqrt(u2_bin - u_bin**2)
r_bin_edge = np.arange(0.0, 1.0, 0.02)
r_bin = 0.5 * (r_bin_edge[1:] + r_bin_edge[:-1])
rho_bin, _, _ = stats.binned_statistic(r, rho, statistic="mean", bins=r_bin_edge)
v_bin, _, _ = stats.binned_statistic(r, v_phi, statistic="mean", bins=r_bin_edge)
P_bin, _, _ = stats.binned_statistic(r, P, statistic="mean", bins=r_bin_edge)
S_bin, _, _ = stats.binned_statistic(r, S, statistic="mean", bins=r_bin_edge)
u_bin, _, _ = stats.binned_statistic(r, u, statistic="mean", bins=r_bin_edge)
rho2_bin, _, _ = stats.binned_statistic(r, rho ** 2, statistic="mean", bins=r_bin_edge)
v2_bin, _, _ = stats.binned_statistic(r, v_phi ** 2, statistic="mean", bins=r_bin_edge)
P2_bin, _, _ = stats.binned_statistic(r, P ** 2, statistic="mean", bins=r_bin_edge)
S2_bin, _, _ = stats.binned_statistic(r, S ** 2, statistic="mean", bins=r_bin_edge)
u2_bin, _, _ = stats.binned_statistic(r, u ** 2, statistic="mean", bins=r_bin_edge)
rho_sigma_bin = np.sqrt(rho2_bin - rho_bin ** 2)
v_sigma_bin = np.sqrt(v2_bin - v_bin ** 2)
P_sigma_bin = np.sqrt(P2_bin - P_bin ** 2)
S_sigma_bin = np.sqrt(S2_bin - S_bin ** 2)
u_sigma_bin = np.sqrt(u2_bin - u_bin ** 2)
# Plot the interesting quantities
figure()
figure(figsize=(7, 7 / 1.6))
line_color = "C4"
binned_color = "C2"
binned_marker_size = 4
scatter_props = dict(
marker=".",
ms=1,
markeredgecolor="none",
alpha=0.5,
zorder=-1,
rasterized=True,
linestyle="none",
)
errorbar_props = dict(color=binned_color, ms=binned_marker_size, fmt=".", lw=1.2)
# Azimuthal velocity profile -----------------------------
subplot(231)
plot(r, v_phi, '.', color='r', ms=0.5)
plot(solution_r, solution_v_phi, '--', color='k', alpha=0.8, lw=1.2)
errorbar(r_bin, v_bin, yerr=v_sigma_bin, fmt='.', ms=8.0, color='b', lw=1.2)
plot([0.2, 0.2], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
plot([0.4, 0.4], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
xlabel("${\\rm{Radius}}~r$", labelpad=0)
ylabel("${\\rm{Azimuthal~velocity}}~v_\\phi$", labelpad=0)
xlim(0,R_max)
plot(r, v_phi, **scatter_props)
plot(solution_r, solution_v_phi, "--", color=line_color, alpha=0.8, lw=1.2)
errorbar(r_bin, v_bin, yerr=v_sigma_bin, **errorbar_props)
plot([0.2, 0.2], [-100, 100], ":", color=line_color, alpha=0.4, lw=1.2)
plot([0.4, 0.4], [-100, 100], ":", color=line_color, alpha=0.4, lw=1.2)
xlabel("Radius $r$")
ylabel("Azimuthal velocity $v_\\phi$")
xlim(0, R_max)
ylim(-0.1, 1.2)
# Radial density profile --------------------------------
subplot(232)
plot(r, rho, '.', color='r', ms=0.5)
plot(solution_r, solution_rho, '--', color='k', alpha=0.8, lw=1.2)
errorbar(r_bin, rho_bin, yerr=rho_sigma_bin, fmt='.', ms=8.0, color='b', lw=1.2)
plot([0.2, 0.2], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
plot([0.4, 0.4], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
xlabel("${\\rm{Radius}}~r$", labelpad=0)
ylabel("${\\rm{Density}}~\\rho$", labelpad=0)
xlim(0,R_max)
ylim(rho0-0.3, rho0 + 0.3)
#yticks([-0.2, -0.1, 0., 0.1, 0.2])
plot(r, rho, **scatter_props)
plot(solution_r, solution_rho, "--", color=line_color, alpha=0.8, lw=1.2)
errorbar(r_bin, rho_bin, yerr=rho_sigma_bin, **errorbar_props)
plot([0.2, 0.2], [-100, 100], ":", color=line_color, alpha=0.4, lw=1.2)
plot([0.4, 0.4], [-100, 100], ":", color=line_color, alpha=0.4, lw=1.2)
xlabel("Radius $r$")
ylabel("Density $\\rho$")
xlim(0, R_max)
ylim(rho0 - 0.3, rho0 + 0.3)
# yticks([-0.2, -0.1, 0., 0.1, 0.2])
# Radial pressure profile --------------------------------
subplot(233)
plot(r, P, '.', color='r', ms=0.5)
plot(solution_r, solution_P, '--', color='k', alpha=0.8, lw=1.2)
errorbar(r_bin, P_bin, yerr=P_sigma_bin, fmt='.', ms=8.0, color='b', lw=1.2)
plot([0.2, 0.2], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
plot([0.4, 0.4], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
xlabel("${\\rm{Radius}}~r$", labelpad=0)
ylabel("${\\rm{Pressure}}~P$", labelpad=0)
plot(r, P, **scatter_props)
plot(solution_r, solution_P, "--", color=line_color, alpha=0.8, lw=1.2)
errorbar(r_bin, P_bin, yerr=P_sigma_bin, **errorbar_props)
plot([0.2, 0.2], [-100, 100], ":", color=line_color, alpha=0.4, lw=1.2)
plot([0.4, 0.4], [-100, 100], ":", color=line_color, alpha=0.4, lw=1.2)
xlabel("Radius $r$")
ylabel("Pressure $P$")
xlim(0, R_max)
ylim(4.9 + P0, P0 + 6.1)
# Internal energy profile --------------------------------
subplot(234)
plot(r, u, '.', color='r', ms=0.5)
plot(solution_r, solution_u, '--', color='k', alpha=0.8, lw=1.2)
errorbar(r_bin, u_bin, yerr=u_sigma_bin, fmt='.', ms=8.0, color='b', lw=1.2)
plot([0.2, 0.2], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
plot([0.4, 0.4], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
xlabel("${\\rm{Radius}}~r$", labelpad=0)
ylabel("${\\rm{Internal~Energy}}~u$", labelpad=0)
xlim(0,R_max)
plot(r, u, **scatter_props)
plot(solution_r, solution_u, "--", color=line_color, alpha=0.8, lw=1.2)
errorbar(r_bin, u_bin, yerr=u_sigma_bin, **errorbar_props)
plot([0.2, 0.2], [-100, 100], ":", color=line_color, alpha=0.4, lw=1.2)
plot([0.4, 0.4], [-100, 100], ":", color=line_color, alpha=0.4, lw=1.2)
xlabel("$Radius $r$")
ylabel("Internal Energy $u$")
xlim(0, R_max)
ylim(7.3, 9.1)
# Radial entropy profile --------------------------------
subplot(235)
plot(r, S, '.', color='r', ms=0.5)
plot(solution_r, solution_s, '--', color='k', alpha=0.8, lw=1.2)
errorbar(r_bin, S_bin, yerr=S_sigma_bin, fmt='.', ms=8.0, color='b', lw=1.2)
plot([0.2, 0.2], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
plot([0.4, 0.4], [-100, 100], ':', color='k', alpha=0.4, lw=1.2)
xlabel("${\\rm{Radius}}~r$", labelpad=0)
ylabel("${\\rm{Entropy}}~S$", labelpad=0)
plot(r, S, **scatter_props)
plot(solution_r, solution_s, "--", color=line_color, alpha=0.8, lw=1.2)
errorbar(r_bin, S_bin, yerr=S_sigma_bin, **errorbar_props)
plot([0.2, 0.2], [-100, 100], ":", color=line_color, alpha=0.4, lw=1.2)
plot([0.4, 0.4], [-100, 100], ":", color=line_color, alpha=0.4, lw=1.2)
xlabel("Radius $r$")
ylabel("Entropy $S$")
xlim(0, R_max)
ylim(4.9 + P0, P0 + 6.1)
# Image --------------------------------------------------
#subplot(234)
#scatter(pos[:,0], pos[:,1], c=v_norm, cmap="PuBu", edgecolors='face', s=4, vmin=0, vmax=1)
#text(0.95, 0.95, "$|v|$", ha="right", va="top")
#xlim(0,1)
#ylim(0,1)
#xlabel("$x$", labelpad=0)
#ylabel("$y$", labelpad=0)
# Information -------------------------------------
subplot(236, frameon=False)
text(-0.49, 0.9, "Gresho-Chan vortex with $\\gamma=%.3f$ at $t=%.2f$"%(gas_gamma,time), fontsize=10)
text(-0.49, 0.8, "Background $\\rho_0=%.3f$"%rho0, fontsize=10)
text(-0.49, 0.7, "Background $P_0=%.3f$"%P0, fontsize=10)
plot([-0.49, 0.1], [0.62, 0.62], 'k-', lw=1)
text(-0.49, 0.5, "$\\textsc{Swift}$ %s"%git, fontsize=10)
text(-0.49, 0.4, scheme, fontsize=10)
text(-0.49, 0.3, kernel, fontsize=10)
text(-0.49, 0.2, "$%.2f$ neighbours ($\\eta=%.3f$)"%(neighbours, eta), fontsize=10)
text_fontsize = 5
text(
-0.49,
0.9,
"Gresho-Chan vortex (2D) with $\\gamma=%.3f$ at $t=%.2f$" % (gas_gamma, time),
fontsize=text_fontsize,
)
text(-0.49, 0.8, "Background $\\rho_0=%.3f$" % rho0, fontsize=text_fontsize)
text(-0.49, 0.7, "Background $P_0=%.3f$" % P0, fontsize=text_fontsize)
plot([-0.49, 0.1], [0.62, 0.62], "k-", lw=1)
text(-0.49, 0.5, "SWIFT %s" % git.decode("utf-8"), fontsize=text_fontsize)
text(-0.49, 0.4, scheme.decode("utf-8"), fontsize=text_fontsize)
text(-0.49, 0.3, kernel.decode("utf-8"), fontsize=text_fontsize)
text(
-0.49,
0.2,
"$%.2f$ neighbours ($\\eta=%.3f$)" % (neighbours, eta),
fontsize=text_fontsize,
)
xlim(-0.5, 0.5)
ylim(0, 1)
xticks([])
yticks([])
savefig("GreshoVortex.png", dpi=200)
tight_layout()
savefig("GreshoVortex.png")
examples/HydroTests/GreshoVortex_3D/plotSolution.py
View file @ b0aee79f
......@@ -22,43 +22,23 @@
# answer
# Parameters
gas_gamma = 5./3. # Gas adiabatic index
rho0 = 1 # Gas density
P0 = 0. # Constant additional pressure (should have no impact on the
# dynamics)
gas_gamma = 5.0 / 3.0 # Gas adiabatic index
rho0 = 1 # Gas density
P0 = 0.0 # Constant additional pressure (should have no impact on the
# dynamics)
# ---------------------------------------------------------------
# Don't touch anything after this.
# ---------------------------------------------------------------
import matplotlib
matplotlib.use("Agg")
from pylab import *
from scipy import stats
import h5py
# Plot parameters
params = {'axes.labelsize': 10,
'axes.titlesize': 10,
'font.size': 12,
'legend.fontsize': 12,
'xtick.labelsize': 10,
'ytick.labelsize': 10,
'text.usetex': True,
'figure.figsize' : (9.90,6.45),
'figure.subplot.left' : 0.045,
'figure.subplot.right' : 0.99,
'figure.subplot.bottom' : 0.05,
'figure.subplot.top' : 0.99,
'figure.subplot.wspace' : 0.15,
'figure.subplot.hspace' : 0.12,
'lines.markersize' : 6,
'lines.linewidth' : 3.,
'text.latex.unicode': True
}
rcParams.update(params)
rc('font',**{'family':'sans-serif','sans-serif':['Times']})
style.use("../../../tools/stylesheets/mnras.mplstyle")
snap = int(sys.argv[1])
......@@ -72,21 +52,27 @@ solution_v_r = zeros(N)
for i in range(N):
if solution_r[i] < 0.2:
solution_P[i] = P0 + 5. + 12.5*solution_r[i]**2
solution_v_phi[i] = 5.*solution_r[i]
solution_P[i] = P0 + 5.0 + 12.5 * solution_r[i] ** 2
solution_v_phi[i] = 5.0 * solution_r[i]
elif solution_r[i] < 0.4:
solution_P[i] = P0 + 9. + 12.5*solution_r[i]**2 - 20.*solution_r[i] + 4.*log(solution_r[i]/0.2)
solution_v_phi[i] = 2. -5.*solution_r[i]
solution_P[i] = (
P0
+ 9.0
+ 12.5 * solution_r[i] ** 2
- 20.0 * solution_r[i]
+ 4.0 * log(solution_r[i] / 0.2)
)
solution_v_phi[i] = 2.0 - 5.0 * solution_r[i]
else:
solution_P[i] = P0 + 3. + 4.*log(2.)
solution_v_phi[i] = 0.
solution_P[i] = P0 + 3.0 + 4.0 * log(2.0)
solution_v_phi[i] = 0.0
solution_rho = ones(N) * rho0
solution_s = solution_P / solution_rho**gas_gamma
solution_u = solution_P /((gas_gamma - 1.)*solution_rho)
solution_s = solution_P / solution_rho ** gas_gamma
solution_u = solution_P / ((gas_gamma - 1.0) * solution_rho)
# Read the simulation data
sim = h5py.File("gresho_%04d.hdf5"%snap, "r")
sim = h5py.File("gresho_%04d.hdf5" % snap, "r")
boxSize = sim["/Header"].attrs["BoxSize"][0]
time = sim["/Header"].attrs["Time"][0]
scheme = sim["/HydroScheme"].attrs["Scheme"]
......@@ -95,14 +81,14 @@ neighbours = sim["/HydroScheme"].attrs["Kernel target N_ngb"]
eta = sim["/HydroScheme"].attrs["Kernel eta"]
git = sim["Code"].attrs["Git Revision"]
pos = sim["/PartType0/Coordinates"][:,:]
x = pos[:,0] - boxSize / 2
y = pos[:,1] - boxSize / 2
vel = sim["/PartType0/Velocities"][:,:]
r = sqrt(x**2 + y**2)
v_r = (x * vel[:,0] + y * vel[:,1]) / r
v_phi = (-y * vel[:,0] + x * vel[:,1]) / r
v_norm = sqrt(vel[:,0]**2 + vel[:,1]**2)
pos = sim["/PartType0/Coordinates"][:, :]
x = pos[:, 0] - boxSize / 2
y = pos[:, 1] - boxSize / 2
vel = sim["/PartType0/Velocities"][:, :]
r = sqrt(x ** 2 + y ** 2)
v_r = (x * vel[:, 0] + y * vel[:, 1]) / r
v_phi = (-y * vel[:, 0] + x * vel[:, 1]) / r
v_norm = sqrt(vel[:, 0] ** 2 + vel[:, 1] ** 2)
rho = sim["/PartType0/Densities"][:]
u = sim["/PartType0/InternalEnergies"][:]
S = sim["/PartType0/Entropies"][:]
......@@ -121,144 +107,183 @@ except:
plot_viscosity = False
# Bin te data
r_bin_edge = np.arange(0., 1., 0.02)
r_bin = 0.5*(r_bin_edge[1:] + r_bin_edge[:-1])
rho_bin,_,_ = stats.binned_statistic(r, rho, statistic='mean', bins=r_bin_edge)
v_bin,_,_ = stats.binned_statistic(r, v_phi, statistic='mean', bins=r_bin_edge)
P_bin,_,_ = stats.binned_statistic(r, P, statistic='mean', bins=r_bin_edge)
S_bin,_,_ = stats.binned_statistic(r, S, statistic='mean', bins=r_bin_edge)
u_bin,_,_ = stats.binned_statistic(r, u, statistic='mean', bins=r_bin_edge)
rho2_bin,_,_ = stats.binned_statistic(r, rho**2, statistic='mean', bins=r_bin_edge)
v2_bin,_,_ = stats.binned_statistic(r, v_phi**2, statistic='mean', bins=r_bin_edge)
P2_bin,_,_ = stats.binned_statistic(r, P**2, statistic='mean', bins=r_bin_edge)
S2_bin,_,_ = stats.binned_statistic(r, S**2, statistic='mean', bins=r_bin_edge)
u2_bin,_,_ = stats.binned_statistic(r, u**2, statistic='mean', bins=r_bin_edge)
rho_sigma_bin = np.sqrt(rho2_bin - rho_bin**2)
v_sigma_bin = np.sqrt(v2_bin - v_bin**2)
P_sigma_bin = np.sqrt(P2_bin - P_bin**2)
S_sigma_bin = np.sqrt(S2_bin - S_bin**2)
u_sigma_bin = np.sqrt(u2_bin - u_bin**2)
r_bin_edge = np.arange(0.0, 1.0, 0.02)
r_bin = 0.5 * (r_bin_edge[1:] + r_bin_edge[:-1])
rho_bin, _, _ = stats.binned_statistic(r, rho, statistic="mean", bins=r_bin_edge)
v_bin, _, _ = stats.binned_statistic(r, v_phi, statistic="mean", bins=r_bin_edge)
P_bin, _, _ = stats.binned_statistic(r, P, statistic="mean", bins=r_bin_edge)
S_bin, _, _ = stats.binned_statistic(r, S, statistic="mean", bins=r_bin_edge)
u_bin, _, _ = stats.binned_statistic(r, u, statistic="mean", bins=r_bin_edge)
rho2_bin, _, _ = stats.binned_statistic(r, rho ** 2, statistic="mean", bins=r_bin_edge)
v2_bin, _, _ = stats.binned_statistic(r, v_phi ** 2, statistic="mean", bins=r_bin_edge)
P2_bin, _, _ = stats.binned_statistic(r, P ** 2, statistic="mean", bins=r_bin_edge)
S2_bin, _, _ = stats.binned_statistic(r, S ** 2, statistic="mean", bins=r_bin_edge)
u2_bin, _, _ = stats.binned_statistic(r, u ** 2, statistic="mean", bins=r_bin_edge)
rho_sigma_bin = np.sqrt(rho2_bin - rho_bin ** 2)
v_sigma_bin = np.sqrt(v2_bin - v_bin ** 2)
P_sigma_bin = np.sqrt(P2_bin - P_bin ** 2)
S_sigma_bin = np.sqrt(S2_bin - S_bin ** 2)
u_sigma_bin = np.sqrt(u2_bin - u_bin ** 2)
if plot_diffusion:
alpha_diff_bin,_,_ = stats.binned_statistic(r, diffusion, statistic='mean', bins=r_bin_edge)
alpha2_diff_bin,_,_ = stats.binned_statistic(r, diffusion**2, statistic='mean', bins=r_bin_edge)
alpha_diff_sigma_bin = np.sqrt(alpha2_diff_bin - alpha_diff_bin**2)
alpha_diff_bin, _, _ = stats.binned_statistic(
r, diffusion, statistic="mean", bins=r_bin_edge
)
alpha2_diff_bin, _, _ = stats.binned_statistic(
r, diffusion ** 2, statistic="mean", bins=r_bin_edge
)
alpha_diff_sigma_bin = np.sqrt(alpha2_diff_bin - alpha_diff_bin ** 2)
if plot_viscosity:
alpha_visc_bin,_,_ = stats.binned_statistic(r, viscosity, statistic='mean', bins=r_bin_edge)
alpha2_visc_bin,_,_ = stats.binned_statistic(r, viscosity**2, statistic='mean', bins=r_bin_edge)
alpha_visc_sigma_bin = np.sqrt(alpha2_visc_bin - alpha_visc_bin**2)
alpha_visc_bin, _, _ = stats.binned_statistic(
r, viscosity, statistic="mean", bins=r_bin_edge
)
alpha2_visc_bin, _, _ = stats.binned_statistic(
r, viscosity ** 2, statistic="mean", bins=r_bin_edge
)
alpha_visc_sigma_bin = np.sqrt(alpha2_visc_bin - alpha_visc_bin ** 2)
# Plot the interesting quantities
figure()
figure(figsize=(7, 7 / 1.6))
line_color = "C4"
binned_color = "C2"
binned_marker_size = 4
scatter_props = dict(
marker=".",
ms=1,
markeredgecolor="none",
alpha=0.1,
zorder=-1,
rasterized=True,
linestyle=<