Multi-scale two-domain numerical modeling of stationary positive DC corona discharge/drift-region coupling

Corona discharge modeling mostly relies on two, distinct, approaches: high-fidelity, numerically challenging, unsteady simulations having high-computational cost or low-fidelity based empirical assumptions such as constant electric field at the emitter electrode. For purpose of steady current predictions, high-fidelity models are very costly to use whilst have limited range validity owing subtle tuned parameters. We propose an intermediate approach: asymptotic multi-scale/two-domain numerical upon generalizing previous axi-symmetrical analysis [1], [2]. show how initial elliptic (electric potential), hyperbolic (charge transport), non-local (photo-ionization) problem can be formulated into two local problems coupled by matching conditions. The approach a multipole expansion radiative photo-ionization source term (in dimensions for cylindrical emitters). analytical conditions derived in [2] result flux continuity boundary domains. These coupling enforced Lagrange multipliers, within variational formulation, leading hierarchy non-linear problems. proposed is both monolithic and two-domains: regions, inner-one associated with corona discharge, outer-one, ion drift region. Numerical convergence validations finite element implementation provided. A comparison various experimental results convincingly demonstrate applicability method, which avoids tuning parameters dedicated each specific configuration, but, contrary, exclusively known measurable physical quantities (e.g., mobilities, coefficient, ionization field, Townsend etc...).