diff --git a/.DS_Store b/.DS_Store index 481cfce..f689667 100644 Binary files a/.DS_Store and b/.DS_Store differ diff --git a/homework3/TH_gen.py b/homework3/TH_gen.py index fba333e..927935e 100644 --- a/homework3/TH_gen.py +++ b/homework3/TH_gen.py @@ -1,82 +1,98 @@ #!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Thu Dec 13 10:53:07 2018 @author: alessia """ import numpy as np import math as m from mpl_toolkits.mplot3d import Axes3D import matplotlib.pyplot as plt from matplotlib import cm from matplotlib.ticker import LinearLocator, FormatStrFormatter #======================================================================================= # # This program generates the initial conditions for Temperature and Heat-rate to # be used to solve the heat-equation with zero homogeneous boundary conditions. + +# The heat-rate is uniformly distributed within a given radius R and zero elsewhere +# The Temperature can either have a zero homogeneous distribution or a Gaussian distrib. + #--------------------------------------------------------------------------------------- N2=100*100 #Number of particles R=0.5 #Radius L=1. #half-lenght of the domain C=1.0 #Constant val for the uniform distrib. of h +TGauss=1 #Gaussian initial distr. for T N=int(m.sqrt(N2)) dx=2*L/N x, y = np.mgrid[-L:L:N*1j, -L:L:N*1j] xy = np.column_stack([x.flat, y.flat]) -T = np.zeros(N2) #homogeneous distr. for Temperature +if(TGauss == 1): + mu = np.array([0.0, 0.0]) + sigma = np.array([.15, .15]) + covariance = np.diag(sigma**2) + T = multivariate_normal.pdf(xy, mean=mu, cov=covariance) + +#create the trivial initial condition for T +else: + T = (np.zeros(N2)) + + +#homogeneous distr. for heat-rate within R h = np.zeros(N2) -h = UniformR(R, N, L, C) #homogeneous distr. for heat-rate within R +h = UniformR(R, N, L, C) z=np.column_stack((xy,T.T,h.T)) #Write the output to file N2 lines 4 columns (xpos, ypos, T, hrate) out_file = open("particles.txt","w") for i in range (0,N2): out_file.write('\n') for j in range(0,4): out_file.write('%.20f' % z[i,j] + '\t') out_file.close() #----------------------Visualization of T and h distributions--------------------------- h = h.reshape(x.shape) T = T.reshape(x.shape) fig = plt.figure() ax = fig.add_subplot(111, projection='3d') surf=ax.plot_surface(x,y,h.T) surf=ax.plot_surface(x,y,T.T,alpha=0.3) plt.show() #======================================================================================= -#----------------------------------------_ END ------------------------------------------ +#---------------------------------------- END ------------------------------------------ #======================================================================================= def UniformR(R, N, L, C): H = np.zeros((N,N)) dx = 2*L/N #Loop over 1/4 of the domain for i in range(0, int(N/2)): x2 = (i*dx-L)**2 for j in range (0, int(N/2)): y2 = (L-j*dx)**2 if(x2+y2<=R): H[i,j] = H[i,N-j-1] = C H[N-i-1,j] = H[N-i-1,N-j-1] = C hh=np.reshape(H,(N*N)) return hh diff --git a/homework3/particles.txt b/homework3/particles.txt new file mode 100644 index 0000000..ca3be69 --- /dev/null +++ b/homework3/particles.txt @@ -0,0 +1,10001 @@ + +-1.00000000000000000000 -1.00000000000000000000 0.00000000000000000035 0.00000000000000000000 +-1.00000000000000000000 -0.97979797979797977892 0.00000000000000000086 0.00000000000000000000 +-1.00000000000000000000 -0.95959595959595955783 0.00000000000000000205 0.00000000000000000000 +-1.00000000000000000000 -0.93939393939393944777 0.00000000000000000481 0.00000000000000000000 +-1.00000000000000000000 -0.91919191919191922668 0.00000000000000001108 0.00000000000000000000 +-1.00000000000000000000 -0.89898989898989900560 0.00000000000000002505 0.00000000000000000000 +-1.00000000000000000000 -0.87878787878787878451 0.00000000000000005565 0.00000000000000000000 +-1.00000000000000000000 -0.85858585858585856343 0.00000000000000012140 0.00000000000000000000 +-1.00000000000000000000 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