Extract PhysicalFace as 2D mesh in fipy - mesh

Question

I created a mesh with Gmsh (a surface with a hole and then extruded it). Now I would like to plot the model in individual slices after a simulation with e.g. the MatplotlibViewer (Mayavi does not work on both my computers). I had hoped that it would be possible to define a new net using mesh.physicalFaces, but if that is possible, I have not figured it out yet. My second attempt was to apply the mesh again with Gmsh up to the Extrude command. But the mesh corresponds not to that of the 3D version. Can somebody give me a clue on this? Also like just another approach to representation.
I am working on Win10, Fipy 3.1.3, Python 3.6
import numpy as np
from fipy import *
#%%
def func_mesh():
mesh = Gmsh3D('''
Geometry.OCCAutoFix = 0;
SetFactory("OpenCASCADE");
x = 1.;
bseg = 0.08;
bs= bseg*x;
ls = 2.1;
cl = 0.01;
radius = 0.006;
// Exterior (bounding box) of mesh
Point(1) = {0, 0, 0, cl};
Point(2) = {0, bs, 0, cl};
Point(4) = { bs, 0, 0, cl};
Point(3) = {bs, bs, 0, cl};
Line(1) = {1, 2};
Line(2) = {2, 3};
Line(3) = {3, 4};
Line(4) = {4, 1};
Line Loop (21) = {1,2,3,4};
//Circle
Point(5) = {bseg/2 - radius, bseg/2, 0, cl};
Point(6) = {bseg/2, bseg/2 + radius, 0, cl};
Point(7) = { bseg/2 + radius, bseg/2, 0, cl};
Point(8) = {bseg/2, bseg/2 - radius, 0, cl};
Point(9) = {bseg/2, bseg/2, 0, cl};
Circle(10) = {5,9,6};
Circle(11) = {6,9,7};
Circle(12) = {7,9,8};
Circle(13) = {8,9,5};
Line Loop(22) = {10,11,12,13};
Plane Surface(40) = {22}; //cycl
Plane Surface(15) = {21, 22}; //Surface with a hole
id[] = Extrude {0, 0, ls} {Surface{15}; Layers{210}; Recombine;};
Surface Loop(2) = {46, 45, 48, 47, 49, 41, 44, 43, 42, 15};
Physical Volume("Vol") = {id[]};
Physical Surface("surf_ges") = {41, 42, 43, 44, 49, 47, 45, 48, 46, 15};
Physical Surface("HX") = {45, 46, 48, 47};
Physical Surface("Extr") = {15};
''')
return mesh
mesh = func_mesh()
x,y,z = mesh.cellCenters
X,Y,Z = mesh.faceCenters
tS = CellVariable(name="storage",
mesh=mesh,
value=367.,
hasOld=True)
submesh = mesh.physicalFaces['Extr']
xsub, ysub = submesh.cellCenters
tSslice = CellVariable(name = 'tSsclice',
mesh = submesh,
value = tS[z== z[0]])
viewer = MatplotlibViewer(vars = tSslice)
The error message for this attemp is: AttributeError: 'binOp' object has no attribute 'cellCenters'.
If I redefine the mesh only until the extrude order I get:
"ValueError: too many values to unpack (expected 2)" because of the shape of tSslice.
I am grateful for any help

Answer 1

submesh is not a Mesh; it's a mask identifying which faces of mesh are included in the surface Extr.
FiPy has no facility for extracting a mesh out of another mesh. It should be feasible to create a Mesh2D using the submesh mask, mesh.vertexCoords, and mesh.faceVertexIDs, but it's not trivial.
In theory, you could invoke Gmsh2D with everything up to Plane Surface(15) = {21, 22}; //Surface with a hole, but I find that doesn't generate the same number of elements as your 3D slice at z == z[0].
Ahah, I see the issue. I thought the Extrude operation resulted in prismatic cells, but it does not. The cells are tetrahedral. Since the cells of mesh do not all have the same tetrahedral geometry, the cells that have their bases on Extr are not all guaranteed to have their centers at z == z[0]. A better way is to use FiPy's CellVariable interpolation to extract the values of tS at the coordinates of tSslice:
from fipy import *
geo = '''
Geometry.OCCAutoFix = 0;
SetFactory("OpenCASCADE");
x = 1.;
bseg = 0.08;
bs= bseg*x;
ls = 2.1;
cl = 0.01;
radius = 0.006;
// Exterior (bounding box) of mesh
Point(1) = {0, 0, 0, cl};
Point(2) = {0, bs, 0, cl};
Point(4) = { bs, 0, 0, cl};
Point(3) = {bs, bs, 0, cl};
Line(1) = {1, 2};
Line(2) = {2, 3};
Line(3) = {3, 4};
Line(4) = {4, 1};
Line Loop (21) = {1,2,3,4};
//Circle
Point(5) = {bseg/2 - radius, bseg/2, 0, cl};
Point(6) = {bseg/2, bseg/2 + radius, 0, cl};
Point(7) = { bseg/2 + radius, bseg/2, 0, cl};
Point(8) = {bseg/2, bseg/2 - radius, 0, cl};
Point(9) = {bseg/2, bseg/2, 0, cl};
Circle(10) = {5,9,6};
Circle(11) = {6,9,7};
Circle(12) = {7,9,8};
Circle(13) = {8,9,5};
Line Loop(22) = {10,11,12,13};
Plane Surface(40) = {22}; //cycl
Plane Surface(15) = {21, 22}; //Surface with a hole
id[] = Extrude {0, 0, ls} {Surface{15}; Layers{210}; Recombine;};
Surface Loop(2) = {46, 45, 48, 47, 49, 41, 44, 43, 42, 15};
Physical Volume("Vol") = {id[]};
Physical Surface("Extr") = {15};
'''
mesh = Gmsh3D(geo + '''
Physical Surface("surf_ges") = {41, 42, 43, 44, 49, 47, 45, 48, 46, 15};
Physical Surface("HX") = {45, 46, 48, 47};
'''
)
submesh = Gmsh2D(geo)
x,y,z = mesh.cellCenters
X,Y = submesh.cellCenters[..., submesh.physicalCells['Extr']]
Z = numerix.ones(X.shape) * z[0]
tS = CellVariable(name="storage",
mesh=mesh,
value=mesh.x * mesh.y * mesh.z,
hasOld=True)
tSslice = CellVariable(name = 'tSsclice',
mesh = submesh)
# interpolate values of tS at positions of tSslice
tSslice[..., submesh.physicalCells['Extr']] = tS(numerix.vstack([X, Y, Z]))
viewer = MatplotlibViewer(vars = tSslice)
Here, I use the same .geo script to define both mesh and submesh. I add the surf_ges and HX physical surfaces only to the definition of mesh, because otherwise all of these faces will be imported into submesh as well, although with an effective z value of 0, so they obscure the faces you're interested in.
Frankly, I think a better way to achieve a slice through 3D data like this is to use either a customized MayaviClient (see the Cahn-Hilliard sphere and sphereDaemon.py for an example) or export with a VTKViewer and then render your data slices with a tool like ParaView, VisIt, or Mayavi.