Appendix: The Discretization of Convection-Diffusion Problems.
Considering the steady convection-diffusion equation:
in a one-dimensional domain:
when the sources are absent, the one-dimensional flow field u is:
where is the diffusion coefficient.
Integration of transport equation over the control volume gives:
Define the convective mass flux per unit area, F:
and diffusion conductance at cell faces, D:
with:
Assuming and the central differencing approach, the transport equation is: