Thin-shell ionosphere model for use in global multi-fluid magnetosphere simulations

The development of a thin-shell ionospheric model is required for simulation of space weather on Earth as well as other planets in the solar system. Our goal is to couple this ionosphere model to multi-fluid solvers in Gkeyll to perform global magnetosphere simulations. Presented is a generalized coordinate solver which finds solutions to the perpendicular Poisson equation on a thin layer of conductivity, weighted by the ionospheric conductivity tensor. A finite volume method is used for its conservative characteristics, also taking advantage of the metric tensor in order to convert between arbitrary 2D logical coordinates and 3D physical coordinates. This provides the ability to use specialized quadrilateral maps which eliminate the spherical-polar singularity at the poles of a sphere. The charge density source is obtained via radial current density along magnetic field lines, and potential on the sphere surface informs potential along field lines further from the ionosphere.