examples.meshing.sphere

An interesting problem is to solve an equation on a 2D geometry that is embedded in 3D space, such as diffusion on the surface of a sphere (with nothing either inside or outside the sphere). This example demonstrates how to create the required mesh.

>>> from fipy import Gmsh2DIn3DSpace, CellVariable, MayaviClient
>>> from fipy.tools import numerix

>>> mesh = Gmsh2DIn3DSpace('''
...     radius = 5.0;
...     cellSize = 0.3;
...
...     // create inner 1/8 shell
...     Point(1) = {0, 0, 0, cellSize};
...     Point(2) = {-radius, 0, 0, cellSize};
...     Point(3) = {0, radius, 0, cellSize};
...     Point(4) = {0, 0, radius, cellSize};
...     Circle(1) = {2, 1, 3};
...     Circle(2) = {4, 1, 2};
...     Circle(3) = {4, 1, 3};
...     Line Loop(1) = {1, -3, 2} ;
...     Ruled Surface(1) = {1};
...
...     // create remaining 7/8 inner shells
...     t1[] = Rotate {{0,0,1},{0,0,0},Pi/2} {Duplicata{Surface{1};}};
...     t2[] = Rotate {{0,0,1},{0,0,0},Pi} {Duplicata{Surface{1};}};
...     t3[] = Rotate {{0,0,1},{0,0,0},Pi*3/2} {Duplicata{Surface{1};}};
...     t4[] = Rotate {{0,1,0},{0,0,0},-Pi/2} {Duplicata{Surface{1};}};
...     t5[] = Rotate {{0,0,1},{0,0,0},Pi/2} {Duplicata{Surface{t4[0]};}};
...     t6[] = Rotate {{0,0,1},{0,0,0},Pi} {Duplicata{Surface{t4[0]};}};
...     t7[] = Rotate {{0,0,1},{0,0,0},Pi*3/2} {Duplicata{Surface{t4[0]};}};
...
...     // create entire inner and outer shell
...     Surface Loop(100)={1,t1[0],t2[0],t3[0],t7[0],t4[0],t5[0],t6[0]};
... ''').extrude(extrudeFunc=lambda r: 1.1 * r) 

>>> x, y, z = mesh.cellCenters 

>>> var = CellVariable(mesh=mesh, value=x * y * z, name="x*y*z") 

>>> if __name__ == '__main__':
...     viewer = MayaviClient(vars=var)
...     viewer.plot()

>>> max(numerix.sqrt(x**2 + y**2 + z**2)) < 5.3 
True
>>> min(numerix.sqrt(x**2 + y**2 + z**2)) > 5.2 
True

Last updated on Nov 20, 2024. Created using Sphinx 7.1.2.