I am modelling convection in spherical section using Finite element method. I am trying to deform 3D cartesian mesh into spherical section with 3480 <= radius <= 6371 km and the angular range in theta and phi is 80 degrees. Please check this image, left side figure is the 3D cartesian mesh which I have and right side is the required deformed geometry of the mesh. I have used some transformation function to deform the mesh but unable to reach final goal. I am looking for some suggestions on algorithm or transformation function to deform the mesh into a spherical section.
Asked
Active
Viewed 320 times
1 Answers
1
Not sure this is really the same, but by eye it looks close enough:
import numpy as np
phi, theta, R = np.ogrid[-40:40:21j, -40:40:21j, 3480:6371:21j]
y, x = np.tan(phi*np.pi/180), np.tan(theta*np.pi/180)
z = R / np.sqrt(x*x + y*y + 1)
y, x = y*z, x*z
from mpl_toolkits.mplot3d import Axes3D
import pylab
fig = pylab.figure(1)
ax = fig.add_subplot(111, projection='3d')
ax.plot_wireframe(x[..., 20], y[..., 20], z[..., 20])
ax.plot_wireframe(0.01*x[..., 20], 0.01*y[..., 20], 0.01*z[..., 20]) # hack to scale z axis
ax.plot_wireframe(x[:, 20, :], y[:, 20, :], z[:, 20, :])
ax.plot_wireframe(x[0, ...], y[0, ...], z[0, ...])
fig.show()
Paul Panzer
- 51,835
- 3
- 54
- 99
-
Thanks. Any reference where I can find derivation of this transformation. – GTR Jun 17 '18 at 07:33
-
@GTR back of envelope, I'm afraid. You make two planes rotate around the x and y axes and intersect them with spheres around the origin and with each other. The rest is basic trigonometry. – Paul Panzer Jun 17 '18 at 08:15
-
How to create a grid which coincides with the longitude and latitude values of the earth for importing datasets (longitude, latitude, parameter) directly to spherical mesh? Above mesh always angularly extended around the equatorial plane. – GTR Jul 01 '18 at 06:21
-
@GTR [This](https://stackoverflow.com/q/30084174/7207392) not good enough? – Paul Panzer Jul 01 '18 at 19:26