A domain-decomposition method to implement electrostatic free boundary conditions in the radial direction for electric discharges

TL;DR

This paper introduces a novel domain-decomposition method to accurately impose electrostatic free boundary conditions in simulations of elongated electric discharges, improving computational efficiency and boundary accuracy.

Contribution

The paper presents a new domain-decomposition approach for implementing free boundary conditions in electrostatic simulations of electric discharges, addressing boundary effects in narrow cylindrical domains.

Findings

Method improves boundary condition accuracy in discharge simulations

Sample implementation demonstrates practical applicability

Reduces computational domain size without sacrificing accuracy

Abstract

At high pressure electric discharges typically grow as thin, elongated filaments. In a numerical simulation this large aspect ratio should ideally translate into a narrow, cylindrical computational domain that envelops the discharge as closely as possible. However, the development of the discharge is driven by electrostatic interactions and, if the computational domain is not wide enough, the boundary conditions imposed to the electrostatic potential on the external boundary have a strong effect on the discharge. Most numerical codes for electric discharges circumvent this problem by either using a wide computational domain or by calculating the boundary conditions by integrating the Green's function of an infinite domain. Here we describe an accurate and efficient method to impose free boundary conditions for an elongated electric discharge. To facilitate the use of our method we provide a sample implementation.