1 import numpy as np
2 import matplotlib.pyplot as plt
3 import matplotlib.mlab as mlab

1 data_vertex = np.loadtxt(‘Velocity0241.dat‘, dtype=float, delimiter=‘,‘, skiprows=1)
2 #data_vertex = np.genfromtxt(‘Velocity0241.dat‘, dtype=float, delimiter=‘,‘,skip_header=1)
3 
4 print(len(data_vertex))
5 
6 X = data_vertex[:,0]
7 Y = data_vertex[:,1]
8 U = data_vertex[:,2]
9 V = data_vertex[:,3]

 1 ‘‘‘
 2 x = X.reshape(89,125)
 3 y = Y.reshape(89,125)
 4 u = U.reshape(89,125)
 5 v = V.reshape(89,125)
 6 ‘‘‘
 7 
 8 x = np.reshape(X,(89,125))
 9 y = np.reshape(Y,(89,125))
10 u = np.reshape(U,(89,125))
11 v = np.reshape(V,(89,125))
12 
13 num_row = x.shape[0]    # get number of rows of Mc
14 num_colume =y.shape[1] # get number of columes of Mc
15 
16 print(num_row)
17 print(num_colume)
18 
19 print(np.shape(x))
20 print(y[0,:])
21 
22 
23 
24 plt.plot(x[:,0])
25 plt.plot(y[0,:])
26 
27 plt.savefig(‘space_linear.png‘, dpi=500)

 1 # streamplot
 2 
 3 import numpy as np
 4 import matplotlib.pyplot as plt
 5 import matplotlib.mlab as mlab
 6 
 7 
 8 fig, ax = plt.subplots(figsize=(10,10))
 9 ax.quiver(y,x,v,u)
10 #ax.quiver(y,x,v,u,color=‘red‘, width=0.005, scale=50)
11 
12 ax.set_title(‘Vortex‘)
13 ax.set_xlabel(‘y‘,size=20)
14 plt.ylabel(‘x‘,size=20)
15 
16 plt.savefig(‘vector_field_of_velocity.png‘,dpi=200,format=‘png‘)
17 
18 plt.show()

 1 # streamplot
 2 
 3 import numpy as np
 4 import matplotlib.pyplot as plt
 5 import matplotlib.mlab as mlab
 6 
 7 fig, ax = plt.subplots(figsize=(6,6))
 8 
 9 x1 = np.linspace(x[0][0],x[88][0],89)
10 y1 = np.linspace(y[0][0],y[0][124],125)
11 
12 ax.streamplot(y1,x1,v,u,13  density=1, linewidth=1, color=‘r‘, arrowsize=2)
14 
15 ax.yaxis.set_ticks([-1.0,-0.75,-0.5,-0.25,0.0,0.25,0.5,0.75,1.0])
16 
17 plt.savefig(‘vortics.png‘，dpi=200,format=‘png‘)
18 
19 plt.show()
20 
21 
22 ‘‘‘
23 fig = plt.figure()
24 ax = fig.gca() # gca get current axis
25 ax.streamplot(y,x,v,u)
26 ‘‘‘

 1 # gradient function in x direction
 2 def dx(M, space): # dx:derivative x
 3     Mc = M.copy()
 4     num_row = Mc.shape[0]    # get number of rows of Mc
 5     num_colume = Mc.shape[1] # get number of columes of Mc
 6     for i in range(num_row):
 7         for j in range(num_colume):
 8             if i == 0:   # left boundary, we use forward difference method
 9                 Mc[i][j] = (M[i+1][j] - M[i][j]) / (space)
10             elif i == (num_row - 1):  # right boundary, we use backward difference method
11                 Mc[i][j] = (M[i][j] - M[i-1][j]) / (space)
12                 
13             else:   # inner points, we use central difference method
14                 Mc[i][j] = (M[i+1][j] - M[i-1][j]) / (2*space)
15     return Mc
16 
17 # gradient function in y direction
18 def dy(M,space):
19     Mc = M.copy()
20     for i in range(num_row):
21         for j in range(num_colume):
22             if j == 0:   # lower boundary, use forward difference
23                 Mc[i][j] = (M[i][j+1] - M[i][j]) / (space)
24             elif j == (num_colume - 1):   #upper boundary, use backward fifference
25                 Mc[i][j] = (M[i][j] - M[i][j-1]) / (space)
26             else:   # inner points, use central difference
27                 Mc[i][j] = (M[i][j+1] - M[i][j-1]) / (2*space)
28     return Mc
29 
30 delta_x = x[1][0] - x[0][0]
31 delta_y = y[0][1] - y[0][0]
32 
33 dudx = dx(u, delta_x)
34 dudy = dy(u, delta_y)
35 dvdx = dx(v, delta_x)
36 dvdy = dy(v, delta_y)
37 
38 print(delta_x)
39 print(delta_y)

1 Div = np.array(dudx) + np.array(dvdy)
2 
3 Curl = np.array(dvdx) - np.array(dudy)

 1 import numpy as np  
 2 import matplotlib.pyplot as plt
 3 
 4 print(np.shape(Div))
 5 
 6 p = plt.pcolormesh(y,x,Div,vmin=-10, vmax=30)
 7 
 8 cb = plt.colorbar(p)
 9 cb.ax.tick_params(labelsize=10)
10 
11 font = {‘family‘ : ‘serif‘,
12         ‘color‘  : ‘darkred‘,
13         ‘weight‘ : ‘normal‘,
14         ‘size‘   : 16,
15         }
16 cb.set_label(‘colorbar‘,fontdict=font)
17 
18 #cb.ax.tick_params(labelsize=32)
19 
20 plt.savefig(‘divergence.png‘,dpi=200)
21 
22 plt.xticks(fontsize=16)
23 plt.yticks(fontsize=8)
24 plt.show()
25 
26 ‘‘‘
27 divergence should be 0 for incompressible flow according to fluid mechanics, but here 
28 it is not 0, that might because the real flow is 3D, but here we just calculate 2d, 
29 in xy plane, and ignore the contribution of the third dimension to divergence
30 ‘‘‘

 1 import numpy as np
 2 import matplotlib.pyplot as plt
 3 
 4 print(np.shape(Curl))
 5 
 6 p = plt.pcolormesh(y,x,Curl) # The rotation is in the opposite direction
 7 
 8 plt.colorbar(p)
 9 
10 plt.savefig(‘curl.png‘,dpi=200)
11 
12 plt.show()