Numerical applications of the advective-diffusive codes for the inner magnetosphere

作者：Aseev N A^*; Shprits Y Y; Drozdov A Y; Kellerman A C

来源：Space Weather-The International Journal of Research and Applications, 2016, 14(11): 993-1010.

DOI：10.1002/2016SW001484

• advective-diffusive codes
• inner magnetosphere
• numerical schemes

In this study we present analytical solutions for convection and diffusion equations. We gather here the analytical solutions for the one-dimensional convection equation, the two-dimensional convection problem, and the one- and two-dimensional diffusion equations. Using obtained analytical solutions, we test the four-dimensional Versatile Electron Radiation Belt code (the VERB-4D code), which solves the modified Fokker-Planck equation with additional convection terms. The ninth-order upwind numerical scheme for the one-dimensional convection equation shows much more accurate results than the results obtained with the third-order scheme. The universal limiter eliminates unphysical oscillations generated by high-order linear upwind schemes. Decrease in the space step leads to convergence of a numerical solution of the two-dimensional diffusion equation with mixed terms to the analytical solution. We compare the results of the third- and ninth-order schemes applied to magnetospheric convection modeling. The results show significant differences in electron fluxes near geostationary orbit when different numerical schemes are used.

• 出版日期2016-11