Cell-Center Equations - Integrate the Diffusion Equation over a cell, and temporally discretize via Backwards Euler:
Face Equations - Flux continuity at every face:
Boundary Face Equations - Robin condition:
Note that:
Unknowns for
are located at the cell centers and the cell faces.
Cell Equations will involve these seven unknowns:
Face Equations will involve the thirteen unknowns from two adjacent
cells:
The ^{ . } terms, on each face of a cell, must still be defined in terms of the 's within that cell.