Sayram: A Positivity-Preserving Open Source 3D Radiation Belt Modeling Code

Standard numerical solutions of multi-dimensional diffusion equations often yield negative, unphysical phase space densities. To address this, we present Sayram, an open-source 3D code for modeling electron flux evolution in Earth’s radiation belts. Using a recently proposed positivity-preserving finite volume method, Sayram ensures physically realistic solutions across a variety of 1D, 2D, and 3D test cases. Its implicit formulation removes constraints from the CFL condition, enabling efficient time stepping. Importantly, the computational overhead associated with ensuring positivity preservation is negligibly small, making Sayram as efficient as other non-positivity-preserving codes based on standard finite difference methods under the same simulation parameters. While developed for radiation belt studies and forecasting, Sayram can also be applied to study general multi-dimensional diffusion processes in other areas, such as wave-particle interactions in planetary magnetospheres and the solar wind. By combining positivity preservation, efficiency, and openness, Sayram provides a robust tool for research across multiple disciplines.