Boundary conditions¶

PyFVTool uses a unified Robin boundary condition form for all boundaries:

\[a \,\nabla\phi \cdot \mathbf{e} + b\,\phi = c\]

where \(\mathbf{e}\) is the outward unit normal. By choosing \(a\), \(b\), and \(c\) you recover all common boundary condition types:

BC type	\(a\)	\(b\)	\(c\)
Dirichlet (fixed value \(\phi_0\))	`0`	`1`	`φ₀`
Neumann (fixed flux \(q\))	`1`	`0`	`q`
No-flux (closed boundary)	`1`	`0`	`0`
Robin	any	any	any

The default boundary condition on all faces is no-flux (\(a=1\), \(b=0\), \(c=0\)).

Setting boundary conditions¶

Boundary conditions are stored on the CellVariable object, in its .BCs attribute.

c = pf.CellVariable(mesh, initial_value)

For a 1D mesh, the available boundaries are .left and .right:

# Dirichlet: fix concentration to 1.0 at the left boundary
c.BCs.left.a = 0.0
c.BCs.left.b = 1.0
c.BCs.left.c = 1.0

# Neumann: fixed flux of 0.5 at the right boundary
c.BCs.right.a = 1.0
c.BCs.right.b = 0.0
c.BCs.right.c = 0.5

For 2D meshes, the available boundaries are .left, .right, .bottom, .top. For 3D meshes, .back and .front are added.

Periodic boundary conditions¶

Periodic BCs can be specified where appropriate. Consult the examples notebooks for details.