@article{AseevShpritsDrozdovetal.2016,
  author    = {Aseev, Nikita and Shprits, Yuri Y. and Drozdov, Alexander and Kellerman, Adam C.},
  title     = {Numerical applications of the advective-diffusive codes for the inner magnetosphere},
  series = {Space Weather: The International Journal of Research and Applications},
  volume    = {14},
  journal   = {Space Weather: The International Journal of Research and Applications},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {1542-7390},
  doi       = {10.1002/2016SW001484},
  pages     = {993 -- 1010},
  year      = {2016},
  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.},
  language  = {en}
}