Modeling Radiation Belt Dynamics Using a Positivity-Preserving Finite Volume Method on General Meshes

Standard finite volume or finite difference methods may produce unphysical negative solutions of phase space density when applied to radiation belt diffusion equation with cross diffusion terms. In this work, we apply a recently proposed positivity-preserving finite volume (PPFV) method to a 2D diffusion problem of radiation belt electrons with both structured and unstructured meshes. Our test using a model problem shows that the new method does not produce unphysical negative solutions with both types of meshes even with strong cross-diffusion terms. By applying the method to the 2D pitch angle and energy diffusion problem, we demonstrate that the method achieves positivity of solutions without requiring excessive number of grid points and shows good agreement with previous results obtained using a layer method. The ability of preserving positivity of the solution with unstructured meshes allows the method to handle complex boundary configurations. Our results suggest that the new PPFV method could be useful in modeling radiation belt diffusion processes or in building a physics-based forecast model.