TY  - JOUR
A1  - Aseev, Nikita
A1  - Shprits, Yuri Y.
A1  - Drozdov, Alexander
A1  - Kellerman, Adam C.
T1  - Numerical applications of the advective-diffusive codes for the inner magnetosphere
JF  - Space Weather: The International Journal of Research and Applications
N2  - 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.
KW  - advective-diffusive codes
KW  - inner magnetosphere
KW  - numerical schemes
Y1  - 2016
U6  - https://doi.org/10.1002/2016SW001484
SN  - 1542-7390
VL  - 14
SP  - 993
EP  - 1010
PB  - American Geophysical Union
CY  - Washington
ER  -