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2D_heat_equation_solver.py
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2D_heat_equation_solver.py
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#!/usr/bin/env python3
# coding: utf-8
'''
Programme pour résoudre l'équation de la chaleur par la méthodes des différences finies
'''
__author__ = 'Nathan Zimniak'
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
from matplotlib.animation import FuncAnimation
from mpl_toolkits import mplot3d
from mpl_toolkits.mplot3d import Axes3D
import time
start_time = time.time()
#Initialisation des constantes
Lx = 201 #Longueur spatiale
Ly = 201 #Largeur spatiale
Nbi = 100001 #Nombre d'itérations temporelles
dx = 1 #Pas spatial suivant x
dy = 1 #Pas spatial suivant y
dt = 1e-2 #Pas temporel
K = 1 #Coefficient de diffusion thermique
#Création du tableau des solutions
T0 = np.zeros((Nbi, Ly, Lx))
Tci = 0 #Condition initiale (température initiale sur toute la plaque)
Tcl1 = 100 #Condition à la limite supérieure de la plaque
Tcl2 = 100 #Condition à la limite inférieure de la plaque
Tcl3 = 100 #Condition à la limite droite de la plaque
Tcl4 = 100 #Condition à la limite gauche de la plaque
T0[:, :, :] = Tci
T0[:, :1, :] = Tcl1
T0[:, (Ly-1):, :] = Tcl2
T0[:, :, (Lx-1):] = Tcl3
T0[:, :, :1] = Tcl4
def finite_difference_method(Z):
''' Calcule la température pour chaque itération temporelle
----------
:param Z: 3D array, tableau des solutions vide
:return: Z, tableau des solutions
----------
'''
for k in range(0, Nbi-1):
for i in range(1, Ly-1):
for j in range(1, Lx-1):
Z[k + 1, i, j] = Z[k][i][j] + K * dt * ((Z[k][i+1][j] + Z[k][i-1][j] - 2*Z[k][i][j])/dx**2 + (Z[k][i][j+1] + Z[k][i][j-1] - 2*Z[k][i][j])/dy**2)
return Z
T = finite_difference_method(T0)
#Affiche le résultat
#Plot (Image 2D)
##plt.style.use('dark_background')
##plt.figure()
##X, Y = np.meshgrid(np.arange(0, Lx), np.arange(0, Ly))
##imageNbi = Nbi-1
##plt.contourf(X, Y, T[imageNbi, :, :], 100, cmap = plt.cm.inferno)
##plt.colorbar()
##plt.xlabel("x")
##plt.ylabel("y")
##plt.title("Température à t = " + str(round(imageNbi*dt,2)) + " s")
##plt.savefig('2D_Heat_Equation.png')
#Plot (Animation 2D)
##plt.style.use('dark_background')
##fig = plt.figure()
##
##def animate(k):
## k=k*100
## plt.clf()
## plt.pcolormesh(T[k, :, :], cmap = plt.cm.inferno)
## plt.colorbar()
## plt.xlabel("x")
## plt.ylabel("y")
## plt.title(f"Température à t = {k*dt:.2f} s")
## return
##
##anim = animation.FuncAnimation(fig, animate, frames = int(Nbi/100), interval = 50, repeat = True)
##
###plt.rcParams['animation.ffmpeg_path'] = 'C:\\ffmpeg\\bin\\ffmpeg.exe'
###Writer = animation.writers['ffmpeg']
###writermp4 = Writer(fps=30, bitrate=1800)
###anim.save("2D_Heat_Equation.mp4", writer=writermp4)
##writergif = animation.PillowWriter(fps=30)
##writergif.setup(fig, "2D_Heat_Equation.gif")
##anim.save("2D_Heat_Equation.gif", writer=writergif)
#Plot (Image 3D)
##plt.style.use('dark_background')
##fig = plt.figure()
##ax = plt.axes(projection = '3d')
##X, Y = np.meshgrid(np.arange(0, Lx), np.arange(0, Ly))
##imageNbi = Nbi-1
##ax.zaxis.set_rotate_label(False)
##surf = ax.plot_surface(X, Y, T[imageNbi, :, :], cmap=plt.cm.inferno)
##ax.set_xlabel("x")
##ax.set_ylabel("y")
##ax.set_zlabel("T (K)", rotation=0)
##ax.w_xaxis.set_pane_color((0.0, 0.0, 0.0, 0.0))
##ax.w_yaxis.set_pane_color((0.0, 0.0, 0.0, 0.0))
##ax.w_zaxis.set_pane_color((0.0, 0.0, 0.0, 0.0))
##ax.grid(False)
##plt.title("Température à t = " + str(round(imageNbi*dt,2)) + " s")
##plt.savefig('3D_Heat_Equation.png')
#Plot (Animation 3D)
plt.style.use('dark_background')
fig = plt.figure()
ax = plt.axes(projection = '3d')
X, Y = np.meshgrid(np.arange(0, Lx), np.arange(0, Ly))
def Animate3D(k):
k=k*100
ax.clear()
ax.set_zlim3d(0, np.max(T))
ax.zaxis.set_rotate_label(False)
ax.plot_surface(X, Y, T[k, :, :], cmap=plt.cm.inferno)
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_zlabel("T (K)", rotation=0)
#fig.set_facecolor('black')
#ax.set_facecolor('black')
ax.w_xaxis.set_pane_color((0.0, 0.0, 0.0, 0.0))
ax.w_yaxis.set_pane_color((0.0, 0.0, 0.0, 0.0))
ax.w_zaxis.set_pane_color((0.0, 0.0, 0.0, 0.0))
ax.grid(False)
plt.title(f"Température à t = {k*dt:.2f} s")
ax.view_init(azim=k/100)
return
anim3D = animation.FuncAnimation(fig, Animate3D, frames = int(Nbi/100), interval = 50, blit = False, repeat = True)
##plt.rcParams['animation.ffmpeg_path'] = 'C:\\ffmpeg\\bin\\ffmpeg.exe'
##Writer = animation.writers['ffmpeg']
##writermp4 = Writer(fps=30, metadata=dict(artist='Me'), bitrate=1800)
##anim3D.save("3D_Schrodinger_Equation.mp4", writer=writermp4)
writergif = animation.PillowWriter(fps=30)
anim3D.save("3D_Heat_Equation.gif", writer=writergif)
print("%s secondes" % (time.time() - start_time))
plt.show()