# -*- coding: utf-8 -*-

#Nom du programme : VanDerWaals

#Auteurs : François Lévrier, Emmanuel Baudin, Arnaud Raoux et la prépa agreg de Montrouge
#Adresse : Departement de physique de l'Ecole Normale Superieure
#		24 rue Lhomond
#		75005 Paris
#Contact : arnaud.raoux@ens.fr
#
#Année de création : 2016 
#Version : 1.10

#Liste des modifications
#v 1.00 : 2016-05-02 Première version complète
#v 1.10 : 2016-05-02 Mise à jour de la mise en page

#LICENCE
#Cette oeuvre, création, site ou texte est sous licence Creative Commons Attribution - Pas d'Utilisation Commerciale 4.0 International. Pour accéder à une copie de cette licence, merci de vous rendre à l'adresse suivante http://creativecommons.org/licenses/by-nc/4.0/ ou envoyez un courrier à Creative Commons, 444 Castro Street, Suite 900, Mountain View, California, 94041, USA.

#Description : 
#Ce programme représente le diagramme PV en unités réduite d'un fluide respectant l'équation d'état de Van der Waals. les références de température, pression et volume sont prises au point critique. Le diagramme trace les courbes isothermes ains que les courbes spinodales et courbes de saturation. 


#import des bibliothèques python
import math
import numpy as np
import scipy
import scipy.integrate
import matplotlib.pyplot as plt
from matplotlib.widgets import Slider, Button, RadioButtons, CheckButtons
from matplotlib import animation

# On charge les tableaux precalcules qui contiennent les donnees pour la courbe spinodale et la courbe de saturation
v_spin=[
0.666740777028,
0.667533928261,
0.668330877052,
0.669131664561,
0.669936332642,
0.670744923866,
0.671557481537,
0.672374049707,
0.673194673196,
0.674019397609,
0.674848269357,
0.675681335675,
0.676518644644,
0.677360245211,
0.67820618721,
0.679056521385,
0.679911299414,
0.680770573932,
0.681634398554,
0.682502827904,
0.683375917637,
0.68425372447,
0.685136306208,
0.686023721773,
0.686916031235,
0.687813295841,
0.688715578051,
0.689622941566,
0.690535451368,
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0.692376176356,
0.693304528223,
0.694238299811,
0.695177563053,
0.696122391395,
0.697072859836,
0.698029044982,
0.698991025085,
0.699958880099,
0.700932691728,
0.70191254348,
0.702898520723,
0.703890710742,
0.704889202801,
0.7058940882,
0.706905460346,
0.707923414819,
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0.70997946434,
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0.712063047581,
0.713115428475,
0.714175014932,
0.71524191988,
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0.717398151193,
0.718487717944,
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0.72069037796,
0.721803730775,
0.722925277559,
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0.725193511063,
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# Creation de la figure
fig, ax = plt.subplots()
plt.subplots_adjust(left=0.15, bottom=0.25)

# On trace la courbe spinodale
plt.plot(v_spin,p_spin,'k--',lw=1)

# On trace la courbe de saturation
plt.plot(v_sat,p_sat,'g--',lw=1)

# Limites
Vr_min=0.4
Vr_max=3.0
Pr_min=0.0
Pr_max=2.5

# Creation de l'axe des abscisses, ici le volume 
# On utilise le meme que pour la courbe de saturation, pour simplifier la recherche des points de croisement
Vr=np.array(v_sat)

# Parametres de la fonction, avec des valeurs par defaut
T0 = 0.9
Tr=T0

# Equation de van der Waals en variables reduites
def VdW_Pr(Tr,Vr):
    return((8.0*Tr/(3.0*Vr-1.0))-3/np.power(Vr,2.0))

# Creation de la fonction a tracer 
Pr = VdW_Pr(Tr,Vr)

# Creation de la trace de la fonction Pr en fonction de Vr. C'est un objet qui est sauvegarde dans 'l'
l, = plt.plot(Vr,Pr, lw=4, color='red')

plt.legend(["Courbe spinodale","Courbe de saturation","Isotherme"])

# Fonction de calcul de la spinodale
def spinodale(Tr):
    local_v_spin=[]
    local_p_spin=[]
    # On calcule la position des zeros de la derivee de p par rapport a v (tangentes horizontales)
    null_dpdv=np.roots([4.0*Tr,-9.0,6.0,-1.0])
    # On ne garde que les valeurs v>1/3, etant donnee que c'est une limite inferieure pour le volume reduit
    null_dpdv=null_dpdv[np.where(null_dpdv>1./3.)]
    # On calcule la pression correspondant a chacun de ces points, et si elle est positive, on trace le point dans le plan (Vr,Pr)
    for v in null_dpdv:
        p=VdW_Pr(Tr,v)
        if (p>0.0):
            local_v_spin.append(v)
            local_p_spin.append(p)
    return(local_v_spin,local_p_spin)

# Fonction de calcul de la courbe de saturation
# Pour calculer la courbe de saturation, on suit la construction de Maxwell
# On explore un domaine de pression "raisonnable" entre les deux pressions correspondant aux tangentes horizontales
def saturation(Tr):
    # On calcule la pression reduite
    Pr=VdW_Pr(Tr,Vr)
    # On determine le domaine ou cette pression est inferieure a la pression de la courbe de saturation
    # On prendra garde, avant d'appeler cette fonction, a verifier que Tr<1
    w=np.where(Pr<np.array(p_sat))
    # On en tire les valeurs extremes, qui sont donc les volumes reduits correspondant aux croisements de l'isotherme avec la courbe de saturation
    V0=Vr[w[0][0]]
    V1=Vr[w[0][len(w[0])-1]]
    # On calcule les pressions correspondantes
    P0=VdW_Pr(Tr,V0)
    P1=VdW_Pr(Tr,V1)
    return([V0,V1],[P0,P1])

# Calcul et affichage du point courant sur la courbe spinodale
local_v_spin,local_p_spin=spinodale(Tr)
lspin,=plt.plot(local_v_spin,local_p_spin,'ko')

# Calcul et affichage du point courant sur la courbe de saturation
local_v_sat,local_p_sat=saturation(Tr)
lsat,=plt.plot(local_v_sat,local_p_sat,'r--',lw=4)

# Specification des limites des axes (xmin,xmax,ymin,ymax)
plt.axis([Vr_min,5,Pr_min,1.5])

# Affichage du point critique
plt.plot(1.0,1.0,'go')

# Affichage des axes
plt.xlabel(r"Volume reduit $V_r$",fontsize=20)
plt.ylabel(r"Pression reduite $P_r$"+"\n",fontsize=20)
plt.title('Transition liquide-vapeur pour un fluide de Van der Waals')
for tick in ax.xaxis.get_major_ticks():tick.label.set_fontsize(15) 
for tick in ax.yaxis.get_major_ticks():tick.label.set_fontsize(15) 

# Creation des barres de modification amplitude et frequence
axcolor = 'lightgoldenrodyellow'
axT = plt.axes([0.25, 0.07, 0.65, 0.03])
sT = Slider(axT, 'Temperature reduite $T_r$', 0.85,1.15, valinit=T0) # Remarquer la valeur initiale f0

# Fonction de mise a jour du graphique
def update(val):
    Tr = sT.val # On recupere la valeur de la barre sfreq comme frequence
    Pr=VdW_Pr(Tr,Vr)
    l.set_ydata(Pr) # On met a jour l'objet 'l' avec ces nouvelles valeurs 
    if(Tr<1.0):
        local_v_spin,local_p_spin=spinodale(Tr)
        lspin.set_xdata(local_v_spin)
        lspin.set_ydata(local_p_spin)
        local_v_sat,local_p_sat=saturation(Tr)
        lsat.set_xdata(local_v_sat)
        lsat.set_ydata(local_p_sat)
        lspin.set_visible(True)
        lsat.set_visible(True)
    else:
        lspin.set_visible(False)
        lsat.set_visible(False)

sT.on_changed(update) # lorsque la barre sT est modifiee, on applique la fonction update


# figManager = plt.get_current_fig_manager()
# figManager.window.showMaximized()
plt.show() # On provoque l'affichage a l'ecran