A 3-D RBF-FD solver for modeling the atmospheric global electric circuit with topography (GEC-RBFFD v1.0)

A numerical model based on radial basis functiongenerated finite differences (RBF-FD) is developed for simulating the global electric circuit (GEC) within the Earth's atmosphere, represented by a 3-D variable coefficient linearelliptic partial differential equation (PDE) in a sphericallyshaped volume with the lower boundary being the Earth's topography and the upper boundary a sphere at 60 km. To ourknowledge, this is (1) the first numerical model of the GECto combine the Earth's topography with directly approximating the differential operators in 3-D space and, related to this,(2) the first RBF-FD method to use irregular 3-D stencils fordiscretization to handle the topography. It benefits from themesh-free nature of RBF-FD, which is especially suitable formodeling high-dimensional problems with irregular boundaries. The RBF-FD elliptic solver proposed here makes nolimiting assumptions on the spatial variability of the coefficients in the PDE (i.e., the conductivity profile), the righthand side forcing term of the PDE (i.e., distribution of current sources) or the geometry of the lower boundary.This work was supported by NSF awards AGS-1135446 and DMS-094581. The National Center for Atmospheric Research is sponsored by the NSF.Publicad