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portion of the boundary where E -n < 0 and requires a Dirichlet boundary condition,
p = 0, everywhere else. Implementing such a mixed boundary condition becomes
problem specific since the portion of boundary where the Dirichlet condition applies
is not known a priori. The mesh must also be sufficiently dense to allow resolution of
the transition from the outflow portion of the boundary to the Dirichlet portion.
The mixed boundary condition is not novel. Cagnoni et al. [4] did include it as part
of the requirements for discharging electrodes in their study, however, the geometries
they investigated did not include a configuration which allows charge stream-tubes
between non-emitting surfaces. The geometry modeled by Martins
does allow
for such a situation but he avoids the problem by applying a zero charge Dirichlet
condition to the collecting electrodes. This approach is less physically accurate and
may introduce errors into the results.