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At high pressure electric discharges typically grow as thin, elongatedfilaments. In a numerical simulation this large aspect ratio should ideallytranslate into a narrow, cylindrical computational domain that envelops thedischarge as closely as possible. However, the development of the discharge isdriven by electrostatic interactions and, if the computational domain is notwide enough, the boundary conditions imposed to the electrostatic potential onthe external boundary have a strong effect on the discharge. Most numericalcodes for electric discharges circumvent this problem by either using a widecomputational domain or by calculating the boundary conditions by integratingthe Green's function of an infinite domain. Here we describe an accurate andefficient method to impose free boundary conditions for an elongated electricdischarge. To facilitate the use of our method we provide a sampleimplementation.

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