Surface charge solver
In order to conserve charge on solid insulators, chombo-discharge has a solver that is defined on the gas-dielectric interface where the surface charge is updated with the incoming flux
\[F_\sigma(\phi) = \sum_{\phi}q_\phi F_{\textrm{EB}}(\phi),\]
where \(q_\phi\) is the charge of a species \(\phi\). This ensures strong conservation on insulating surfaces.