[celestial]

First some background to familiarize the reader.

let V be the voltage and rho the volume charge density in air and epsilon the permittivity of air

solve (fvm::laplacian(V)) is implicit for unknown V in the dielectric

and

solve (fvm::laplacian(V)==rho/epsilon)

is implicit for unknown V in the dielectric

now let En = -snGrad(V)

be the electric field normal to the interface on the air side

and E1n = -snGrad(V)

be the electric field normal to the interface on the dielectric side

the boundary condition is epsilon*En-epsilon1*E1n = sigma

where sigma is the surface charge density on the interface and epsilon1 is the permittivity of the dielectric

Next for the transport equation shown for an ion with number density np, E=-grad(V) and

the flux Fp = mu*np*E - Dp*fvm::grad(np) + np*U

where mu is mobility De the Einstein constant and U the drift velocity. The source S is a term involving recombination, attachment and ionization. It depends on np but np is treated explicity in this source term.

we have

solve(fvm::ddt(np) + fvm::div(Fp) == S)

is implicit for unknown np including np found in Fp

Now at the interface, the normal component of Fp = min(En,0) -np*vthp/4
where vthp is just a thermal constant.

none of the standard boundary condition found in the user guide work including "calculated".
Even though I have written the above mathematical equations using partial OpenFoam syntax, I am a total loss as how to go about coding them.

Any reply welcome

Thanks,
Marc

[celestial]

Never mind with this thread I started. For those interested, I provide a partial answer in

On fairly general BC's