plotSolution.py

Go to the documentation of this file.

#!/usr/bin/env python3
 
 
# Computes the analytical solution of the Noh problem and plots the SPH answer
 
 
# Parameters
gas_gamma = 5.0 / 3.0  # Polytropic index
rho0 = 1.0  # Background density
P0 = 1.0e-6  # Background pressure
v0 = 1
 
import matplotlib
 
matplotlib.use("Agg")
 
import matplotlib.pyplot as plt
from scipy import stats
import numpy as np
import sys
 
from peano4.api.toolbox.particles.postprocessing.ParticleVTUReader import ParticleVTUReader
 
if len(sys.argv) < 2:
    time = 0.2
else:
    time = float(sys.argv[1])
 
pvdfile = "particles.pvd"
reader = ParticleVTUReader(pvdfile=pvdfile, snapshot_time=time)
partData = reader.load()
time = reader.get_snapshot_time()
 
# show me what particle fields are stored
#  partData.show_attribute_list()
 
x = partData.x[:, 0]
y = partData.x[:, 1]
vx = partData.v[:, 0]
vy = partData.v[:, 1]
u = partData.u
#  S = partData.S # doesn't exist yet?
P = partData.pressure
rho = partData.density
 
 
r = np.sqrt((x - 1.0) ** 2 + (y - 1.0) ** 2)
v = -np.sqrt(vx**2 + vy**2)
 
# Bin the data
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, 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**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)
 
# Analytic solution
N = 1000  # Number of points
 
x_s = np.arange(0, 2.0, 2.0 / N) - 1.0
rho_s = np.ones(N) * rho0
P_s = np.ones(N) * rho0
v_s = np.ones(N) * v0
 
# Shock position
u0 = rho0 * P0 * (gas_gamma - 1)
us = 0.5 * (gas_gamma - 1) * v0
rs = us * time
 
# Post-shock values
rho_s[np.abs(x_s) < rs] = rho0 * ((gas_gamma + 1) / (gas_gamma - 1)) ** 2
P_s[np.abs(x_s) < rs] = 0.5 * rho0 * v0**2 * (gas_gamma + 1) ** 2 / (gas_gamma - 1)
v_s[np.abs(x_s) < rs] = 0.0
 
# Pre-shock values
rho_s[np.abs(x_s) >= rs] = rho0 * (1 + v0 * time / np.abs(x_s[np.abs(x_s) >= rs]))
P_s[np.abs(x_s) >= rs] = 0
v_s[x_s >= rs] = -v0
v_s[x_s <= -rs] = v0
 
# Additional arrays
u_s = P_s / (rho_s * (gas_gamma - 1.0))  # internal energy
s_s = P_s / rho_s**gas_gamma  # entropic function
 
# Plot the interesting quantities
plt.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=0.2,
    zorder=-1,
    rasterized=True,
    linestyle="none",
)
 
errorbar_props = dict(color=binned_color, ms=binned_marker_size, fmt=".", lw=1.2)
 
rows = 2
cols = 2
 
# Velocity profile --------------------------------
plt.subplot(rows, cols, 1)
plt.plot(r, v, **scatter_props)
plt.plot(x_s, v_s, "--", color=line_color, alpha=0.8, lw=1.2)
plt.errorbar(r_bin, v_bin, yerr=v_sigma_bin, **errorbar_props)
plt.xlabel("${\\rm{Radius}}~r$", labelpad=0)
plt.ylabel("${\\rm{Velocity}}~v_r$", labelpad=-4)
plt.xlim(0, 0.5)
plt.ylim(-1.2, 0.4)
 
# Density profile --------------------------------
plt.subplot(rows, cols, 2)
plt.plot(r, rho, **scatter_props)
plt.plot(x_s, rho_s, "--", color=line_color, alpha=0.8, lw=1.2)
plt.errorbar(r_bin, rho_bin, yerr=rho_sigma_bin, **errorbar_props)
plt.xlabel("${\\rm{Radius}}~r$", labelpad=0)
plt.ylabel("${\\rm{Density}}~\\rho$", labelpad=0)
plt.xlim(0, 0.5)
plt.ylim(0.95, 19)
 
# Pressure profile --------------------------------
plt.subplot(rows, cols, 3)
plt.plot(r, P, **scatter_props)
plt.plot(x_s, P_s, "--", color=line_color, alpha=0.8, lw=1.2)
plt.errorbar(r_bin, P_bin, yerr=P_sigma_bin, **errorbar_props)
plt.xlabel("${\\rm{Radius}}~r$", labelpad=0)
plt.ylabel("${\\rm{Pressure}}~P$", labelpad=0)
plt.xlim(0, 0.5)
plt.ylim(-0.5, 11)
 
# Internal energy profile -------------------------
plt.subplot(rows, cols, 4)
plt.plot(r, u, **scatter_props)
plt.plot(x_s, u_s, "--", color=line_color, alpha=0.8, lw=1.2)
plt.errorbar(r_bin, u_bin, yerr=u_sigma_bin, **errorbar_props)
plt.xlabel("${\\rm{Radius}}~r$", labelpad=0)
plt.ylabel("${\\rm{Internal~Energy}}~u$", labelpad=0)
plt.xlim(0, 0.5)
plt.ylim(-0.05, 0.8)
 
plt.tight_layout()
 
fname = f"NohProfile{time:.4f}.png"
plt.savefig(fname, dpi=200)
print("saved", fname)