Core Concepts
This paper presents a computationally efficient mixed-dimensional model for solving the electrostatic equation in coupled domains with different dielectric constants, specifically focusing on thin inclusions within a larger 3D domain, and validates the model against analytical solutions and fully resolved 3D simulations.
Stats
The gas domain is assumed to have a much smaller radius than its length (R << L).
The total charge q in the gas domain is assumed to be constant over sections orthogonal to its centerline.
The fluctuations of functions around their integral mean on the boundary of each section are assumed to have zero mean.
The flux of the electric field across the section at the tip of the thin inclusion is assumed to be negligible.