We call a flux purely convective if the diffusive part, driven by the
concentration gradient, vanishes, i.e. 
. This lack of
dissipation may cause serious numerical troubles. The resulting PDE
equation is not a second order differential equation.
Here 
denotes a velocity. A central difference approximation of this
term in the form 
, using linearly interpolated values 
and
, is known to produce oscillations or wiggles in the
solution [Mit80] - convergence cannot be guaranteed.
Remedy is expected from upwinding schemes, see for instance [Kre87],
where the -term is approximated in the form
. In the limit the upwinding parameter is
for 
and 
for
.
For the partial derivatives in (3.4-29), (3.4-30) we apply
again the difference approximations (3.4-24) and
(3.4-25). The values of the electrostatic potential 
and
the metric coefficients 
, 
, 
, and 
are available at the
grid points. The mobility 
and the velocity 
(from other driving
forces) that are explicitly available at the center point and may depend on
all concentrations.
