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I'm fairly new to FiPy and I'm currently facing an issue of which I am sure can be solved easily: I want to solve a 3D steady flow of the form:

    eq = ( DiffusionTerm(var=u) ==  -(1/mu) * dP + g_acc * (rho/mu) * ymax )

Where velocity u is in the y-direction and where du/dy = 0. I would like to let the PDE solve within a subdomain of the entire 3D mesh, meaning that:

  • 0 <= X < Boundary_1, u=0.
  • Boundary_1 <= X < Boundary_2, u = PDE solution
  • Boundary_2 <= X < Lx, u = 0.

Currently I have tried the following:

mesh = Grid3D(dx=dx, dy=dy, dz=dz, Lx=(Lx-0), Ly =(ymax-ymin), Lz=(zmax-zmin))
u = CellVariable(name = "velocity", mesh = mesh)

X, Y, Z = mesh.cellCenters
LeftWall = (X <= xBoundary_left)
RightWall = (X > xBoundary_right)
FrontWall = (mesh.facesFront)
BackWall = (mesh.facesBack)

u.constrain(0., where=LeftWall)
u.constrain(0., where=RightWall)
u.constrain(0., where=FrontWall)
u.constrain(0., where=BackWall)

Which leads to a solution of image 1 (see attached image). The boundary conditions for the X variable are not taken into account as I would like, as you can see in the example in image 2, where only the PDE domain is shown. What I am looking for is a way to define the boundary conditions at the faces of the subdomain in such a way that it does not 'crop' the solution, but rather only solves the PDE for that subdomain. If it is possible to 'stitch' meshes together that include a Cellvariable u that has value 0 for two meshes and the value of the solved PDE for one mesh, that would be great as well!

I have tried working with inner boundary conditions in the form of an Implicit source, but that ended up in different errors.

Any help would be much appreciated!

Michiel Hickey
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1 Answers1

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FiPy constraints do not work on internal faces.

In our own work, rather than only solving an equation in a subdomain, we modify the coefficients to cause different behaviors to dominate in different subdomains. Conservation of momentum and conservation of mass don't suddenly stop being true; rather different conditions lead to, e.g., different Reynolds numbers.

It is possible to solve different equations on different meshes and communicate between them. See, e.g.,

jeguyer
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