On the modelling of highly anisotropic diffusion for electron radiation belt dynamic codes

• Published in: Computer physics communications 2020-09, Vol.254, p.107342, Article 107342
• Main Authors: Dahmen, Nour, Rogier, François, Maget, Vincent
• Format: Article
• Language: English
• Subjects: Anisotropic diffusion equation; Discrete maximum principle; Engineering Sciences; Finite volume method; Monotony; Physics; Radiation belts
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/j.cpc.2020.107342

Electron radiation belts are regions surrounding Earth, filled with highly energetic electrons and overlapping the majority of satellite orbits. Their multi-scale and rapidly evolving dynamics are modelled by the mean of a diffusion equation involving a highly anisotropic and inhomogeneous diffusion tensor. Finite difference based methods have been the preferred method of discretization in physical codes, starting from ONERA’s Salammbô-Electron model, the pioneering 3-dimensional code in the radiation belts community. This choice however does not prevent several numerically induced constraints impacting the reliability of the code as well as its computational cost. Thus in this paper we present the outcome of our investigation to improve Salammbô’s numerical core. In particular, we present our special diffusion frame and its numerically induced limitations on our finite difference based scheme. Then we test potential alternative finite volume schemes with physically relevant properties and we finally highlight with a real case simulation the contribution of the positivity preserving scheme to evaluate the impact of cross diffusion.