@article{doi:10.1002/2016SW001484,
author = {Aseev, N. A. and Shprits, Y. Y. and Drozdov, A. Y. and Kellerman, A. C.},
title = {Numerical applications of the advective-diffusive codes for the inner magnetosphere},
year={2016},
journal = {Space Weather},
volume = {14},
number = {11},
pages = {993-1010},
keywords = {advective-diffusive codes, inner magnetosphere, numerical schemes},
doi = {10.1002/2016SW001484},
url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2016SW001484},
eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2016SW001484},
abstract = {Abstract 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.}
}