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

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...

Full description

Saved in:
Bibliographic Details
Published in:Space Weather 2016-11, Vol.14 (11), p.993-1010
Main Authors: Aseev, N. A., Shprits, Y. Y., Drozdov, A. Y., Kellerman, A. C.
Format: Article
Language:English
Subjects:
advective‐diffusive codes
Belts
Convection
Convection modes
Convergence
Diffusion
Diffusion equations
Economic models
Electron density
Electron flux
Electron radiation
Fokker-Planck equation
inner magnetosphere
Magnetosphere
Magnetospheres
Magnetospheric convection
Mathematical analysis
Mathematical models
Numerical schemes
Oscillations
Radiation
Two-dimensional analysis
Upwind schemes (mathematics)
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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. Key Points A set of convenient analytical solutions for testing codes for the inner magnetosphereis presented The basic features of the numerical schemes of the VERB‐4D code are demonstrated The order of numerical schemes has significant influence on magnetospheric convection modeling
ISSN:1542-7390
1539-4964
1542-7390
DOI:10.1002/2016SW001484