From 5473ade7817b86bfad632acc90b821db9d2eb5d6 Mon Sep 17 00:00:00 2001 From: mbui Date: Tue, 9 May 2023 22:19:36 +0200 Subject: [PATCH] TP1 Intro Modelisation --- EA.py | 31 +++++++++++++++++++++ EP.py | 42 +++++++++++++++++++++++++++++ Fig/EA_CFL =0.2.png | Bin 0 -> 19533 bytes Fig/EA_CFL =0.5.png | Bin 0 -> 18463 bytes Fig/EA_CFL =0.8.png | Bin 0 -> 19408 bytes Fig/EP_CFL =0.2.png | Bin 0 -> 22974 bytes Fig/EP_CFL =0.5.png | Bin 0 -> 16816 bytes Fig/EP_CFL =0.8.png | Bin 0 -> 19116 bytes Fig/u=X(x)T=10_CFL =0.8.png | Bin 0 -> 27058 bytes Fig/u=X(x)T=1_CFL =0.8.png | Bin 0 -> 21917 bytes Fig/u=X(x)T=5_CFL =0.8.png | Bin 0 -> 25360 bytes Fig/u=f(x)CFL =0.2.png | Bin 0 -> 67514 bytes Fig/u=f(x)CFL =0.5.png | Bin 0 -> 61374 bytes Fig/u=f(x)CFL =0.8.png | Bin 0 -> 57259 bytes Fig/u=f(x)T=10_CFL =0.2.png | Bin 0 -> 29337 bytes Fig/u=f(x)T=10_CFL =0.5.png | Bin 0 -> 26713 bytes Fig/u=f(x)T=10_CFL =0.8.png | Bin 0 -> 24896 bytes Fig/u=f(x)T=1_CFL =0.2.png | Bin 0 -> 21450 bytes Fig/u=f(x)T=1_CFL =0.5.png | Bin 0 -> 20549 bytes Fig/u=f(x)T=1_CFL =0.8.png | Bin 0 -> 19497 bytes Fig/u=f(x)T=5_CFL =0.2.png | Bin 0 -> 25661 bytes Fig/u=f(x)T=5_CFL =0.5.png | Bin 0 -> 23565 bytes Fig/u=f(x)T=5_CFL =0.8.png | Bin 0 -> 21872 bytes tp1.py | 52 ++++++++++++++++++++++++++++++++++++ tp1_lib.py | 34 +++++++++++++++++++++++ 25 files changed, 159 insertions(+) create mode 100644 EA.py create mode 100644 EP.py create mode 100644 Fig/EA_CFL =0.2.png create mode 100644 Fig/EA_CFL =0.5.png create mode 100644 Fig/EA_CFL =0.8.png create mode 100644 Fig/EP_CFL =0.2.png create mode 100644 Fig/EP_CFL =0.5.png create mode 100644 Fig/EP_CFL =0.8.png create mode 100644 Fig/u=X(x)T=10_CFL =0.8.png create mode 100644 Fig/u=X(x)T=1_CFL =0.8.png create mode 100644 Fig/u=X(x)T=5_CFL =0.8.png create mode 100644 Fig/u=f(x)CFL =0.2.png create mode 100644 Fig/u=f(x)CFL =0.5.png create mode 100644 Fig/u=f(x)CFL =0.8.png create mode 100644 Fig/u=f(x)T=10_CFL =0.2.png create mode 100644 Fig/u=f(x)T=10_CFL =0.5.png create mode 100644 Fig/u=f(x)T=10_CFL =0.8.png create mode 100644 Fig/u=f(x)T=1_CFL =0.2.png create mode 100644 Fig/u=f(x)T=1_CFL =0.5.png create mode 100644 Fig/u=f(x)T=1_CFL =0.8.png create mode 100644 Fig/u=f(x)T=5_CFL =0.2.png create mode 100644 Fig/u=f(x)T=5_CFL =0.5.png create mode 100644 Fig/u=f(x)T=5_CFL =0.8.png create mode 100644 tp1.py create mode 100644 tp1_lib.py diff --git a/EA.py b/EA.py new file mode 100644 index 0000000..68cd8cb --- /dev/null +++ b/EA.py @@ -0,0 +1,31 @@ +import numpy as np +import sympy +import matplotlib.pyplot as plt + +def EA1(xi,alpha): + return 1-np.sqrt(1-2*alpha*(1-alpha)*(1-np.cos(xi))) + +def EA2(xi,alpha): + return 1-np.sqrt(1-(alpha**2)*(1-alpha**2)*((1-np.cos(xi))**2)) + +def EA3(xi,alpha): + theta=xi/2 + return 1-np.sqrt((1-2*alpha*(np.sin(theta)**2)*(1-(1-alpha)*(np.cos(theta)**2)))**2 + +(2*alpha*np.cos(theta)*np.sin(theta)*(1+(1-alpha)*(np.sin(theta)**2)))**2) + +xi = np.linspace(0,np.pi/8,1000) + +for alpha in [0.2,0.5,0.8]: + fig=plt.figure(1) + plt.title(r"Erreur d'amplitude en fonction de $\zeta$ pour CFL = "+str(alpha)) + plt.xlabel(r'$\zeta$') + plt.ylabel(r'$E_A$') + plt.axis([-0.02 , np.pi/8+0.02 , 1e-15, 1e-1]) + plt.semilogy(xi,EA1(xi,alpha),'-g',label="Schema 1") + plt.semilogy(xi,EA2(xi,alpha),'-b',label="Schema 2") + plt.semilogy(xi,EA3(xi,alpha),'-r',label="Schema 3") + plt.legend() + plt.grid(True) + plt.show(block=False) + #plt.savefig("EA"+"_CFL ="+str(alpha)+".png") + plt.close('all') diff --git a/EP.py b/EP.py new file mode 100644 index 0000000..da90ab3 --- /dev/null +++ b/EP.py @@ -0,0 +1,42 @@ +import numpy as np +import math +import matplotlib.pyplot as plt +import EA + +def acos(X): + Y=np.zeros_like(X) + for i in range(len(X)): + Y[i]=math.acos(X[i]) + return Y + +def EP1(xi,alpha): + return alpha*xi - acos((1-alpha*(1-np.cos(xi))) + /(1-EA.EA1(xi,alpha))) + +def EP2(xi,alpha): + return alpha*xi - acos((1-(alpha**2)*(1-np.cos(xi))) + /(1-EA.EA2(xi,alpha))) + +def EP3(xi,alpha): + theta=xi/2 + return alpha*xi - acos((1-2*alpha*(np.sin(theta)**2)*(1-(1-alpha)*(np.cos(theta)**2))) + /(1-EA.EA3(xi,alpha))) + +xi = np.linspace(0,np.pi/8,1000) + +#print(EP1(xi,0.5),"\n",EP3(xi,0.5)) + +for alpha in [0.2,0.5,0.8]: + fig=plt.figure(1) + plt.title(r"Erreur de phase en fonction de $\zeta$ pour CFL = "+str(alpha)) + plt.xlabel(r'$\zeta$') + plt.ylabel(r'$E_\phi$') + plt.axis([-0.02 , np.pi/8+0.02 , -0.0010, 0.0030]) + plt.plot(xi,abs(EP1(xi,alpha)),'-g',label="Schema 1") + plt.plot(xi,abs(EP2(xi,alpha)),'-b',label="Schema 2") + plt.plot(xi,abs(EP3(xi,alpha)),'-r',label="Schema 3") + plt.legend(loc='upper left') + plt.grid(True) + plt.show(block=False) + #plt.savefig("EP"+"_CFL ="+str(alpha)+".png") + plt.close('all') \ No newline at end of file diff --git a/Fig/EA_CFL =0.2.png b/Fig/EA_CFL =0.2.png new file mode 100644 index 0000000000000000000000000000000000000000..cd66bd5a7a10d95fb3f543329557df05adf39dd7 GIT binary patch literal 19533 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alpha*(U0[1:J+1]-U0[0:J]) + return U1 + +def schema2(U0,J,alpha): + U0=np.append(U0[J-2],U0) + U0=np.append(U0,U0[1]) + U1=U0[1:J+1]-(alpha/2)*(U0[2:J+2]-U0[0:J])+(0.5*alpha**2)*(U0[2:J+2]-2*U0[1:J+1]+U0[0:J]) + return U1 + +def schema3(U0,J,alpha): + U0=np.append(U0[J-2],U0) + U0=np.append(U0[J-3],U0) + U0=np.append(U0,U0[1]) + U1=U0[2:J+2]-alpha*(U0[2:J+2]-U0[1:J+1])-((alpha/4)*(1-alpha)*(U0[3:J+3]-U0[2:J+2]-U0[1:J+1]+U0[0:J])) + return U1