Hi FiPy,
I am toying around with the following problem, suppose there is a vector field
v=(x,y) and I am looking to compute div(v)=2 with FiPy. I know that the
.divergence property is for FaceVariables but suppose we need to build the
vector field from a CellVariable. As far as I know, from the CellVariable I can
get face values with .faceValue. So I looked to test this sort of procedure
with the simple case stated above.
Build the mesh, the cellVariable and give it the values x,y (here cellCenters):
>>> m=Grid2D(nx=4,ny=4)
>>> v=CellVariable(mesh=m,rank=1)
>>> v[0]=m.x
>>> v[1]=m.y
Interpolate the faceValues (I expected in this case, these should be
faceCenters, clearly theres a difference):
>>> vfv=v.faceValue
>>> vfv[0].value
array([ 0.5, 1.5, 2.5, 3.5, 0.5, 1.5, 2.5, 3.5, 0.5, 1.5, 2.5,
3.5, 0.5, 1.5, 2.5, 3.5, 0.5, 1.5, 2.5, 3.5, 0.5, 1. ,
2. , 3. , 3.5, 0.5, 1. , 2. , 3. , 3.5, 0.5, 1. , 2. ,
3. , 3.5, 0.5, 1. , 2. , 3. , 3.5])
>>> m.faceCenters[0].value
array([ 0.5, 1.5, 2.5, 3.5, 0.5, 1.5, 2.5, 3.5, 0.5, 1.5, 2.5,
3.5, 0.5, 1.5, 2.5, 3.5, 0.5, 1.5, 2.5, 3.5, 0. , 1. ,
2. , 3. , 4. , 0. , 1. , 2. , 3. , 4. , 0. , 1. , 2. ,
3. , 4. , 0. , 1. , 2. , 3. , 4. ])
>>> vfv[0].value-m.faceCenters[0].value
array([ 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ,
0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.5, 0. ,
0. , 0. , -0.5, 0.5, 0. , 0. , 0. , -0.5, 0.5, 0. , 0. ,
0. , -0.5, 0.5, 0. , 0. , 0. , -0.5])
When I compute the divergence from “interpolated” face values versus the
faceCenters I am getting the following:
>>> vfv.divergence.value
array([ 1. , 1.5, 1.5, 1. , 1.5, 2. , 2. , 1.5, 1.5, 2. , 2. ,
1.5, 1. , 1.5, 1.5, 1. ])
>>> m.faceCenters.divergence.value
array([ 2., 2., 2., 2., 2., 2., 2., 2., 2., 2., 2., 2., 2.,
2., 2., 2.])
The interpolated face values are not giving what I would expect for the
divergence. This worries me for when I go to compute more complicated
quantities. Any pointers are much appreciated. As always I look forward to
hearing more.
Best,
Kyle
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