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.Comment: 21 pages, 4 figures, a movie and a sample code in python. A new
Appendix has been adde
