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# -*- coding: utf-8 -*-
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import numpy as np
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import matplotlib.pyplot as plt
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class Spreader_2D_adim:
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"""Spreader 2D adimensionné"""
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# Variables
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K = 1
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S = 1
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B = 1
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Q = 0
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# Initialisation
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def __init__(self, K, S, B, Q=0):
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"""Constructeur de Spreader_2D_adim"""
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self.K = K
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self.S = S
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self.B = B
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self.Q = Q
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# Accesseurs
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def set_K(self, K):
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self.K = K
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def set_S(self, S):
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self.S = S
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def set_B(self, B):
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self.B = B
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def set_Q(self, Q):
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self.Q = Q
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def get_K(self, K):
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return self.K
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def get_S(self, S):
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return self.S
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def get_B(self, B):
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return self.B
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def get_Q(self, Q):
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return self.Q
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# Méthodes privées
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def _beta_old(self, n, Y):
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F = self.K * self.S
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S = self.S
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B = self.B
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P = B/F
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PI = np.pi
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return 2*np.sinc(n/S)*((1/S - P/(n*PI))*np.exp(-(2-Y)*F*n*PI/S)
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+ (1/S + P/(n*PI))*np.exp(-Y*F*n*PI/S))\
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/ (F*(P + n*PI*np.tanh(F*n*PI/S)/S)
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* (1 + np.exp(-2*F*n*PI/S)))
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def _beta(self, n, Y):
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Knpi = self.K*n*np.pi
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return 2*np.sinc(n/self.S)*((Knpi - self.B)*np.exp(-Knpi*(2-Y))
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+ (Knpi + self.B)*np.exp(-Knpi*Y))\
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/ (self.S*Knpi*(self.B + Knpi*np.tanh(Knpi))
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* (1+np.exp(-2*Knpi)))
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# Méthodes publiques
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def theta_ss(self, X, Y, N=100):
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"""Température en régime permanent"""
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f = (1 - Y + 1/self.B)/self.S
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g = self.Q*(1/self.B + (1 - 0.5*Y**2))
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return f + g + sum([self._beta_old(n, Y)*np.cos(n*np.pi*X) for n in range(1, N+1)])
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# Execution en temps que main
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if __name__ == "__main__":
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K = 0.025
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S = 4
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B = 0.005
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Q = 0
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spreader = Spreader_2D_adim(K, S, B, Q)
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X = np.linspace(0, 1, 20)
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Y = np.linspace(0, 1, 20)
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XX, YY = np.meshgrid(X, Y)
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plt.figure()
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plt.contourf(XX, YY, spreader.theta_ss(XX, YY))
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plt.colorbar()
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