On the approximation of the diffusion operator in the ionosphere model with conserving the direction of geomagnetic field
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Pavel A. Ostanin
Abstract
New methods for constructing an approximation of the diffusion operator for the two-dimensional equation of the ambipolar diffusion process in the F layer of the Earth's ionosphere are presented. This equation is solved in the framework of modelling the global thermosphere and ionosphere dynamics (for the altitudes from 90 to 500 km). The proposed schemes have finite-difference versions of the integral identity, which is a property of differential diffusion equation and which represents the geometric properties of the process (diffusion proceeds along the magnetic field lines of the Earth). The stability of the proposed schemes is analyzed, as well as the accuracy estimates are obtained on the base of the model analytical solution and during the calculations with physically realistic data. A comparison is made with the second-order finite-difference scheme developed earlier for solving the same problem.
Acknowledgment
The author is grateful to V. V. Shashkin for his detailed acquaintance with the paper and valuable remarks, to D. V. Kulyamin for help in the preparation of the paper, and also to V. P. Dymnikov for the formulation of the problem.
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Funding: The research was supported by the Moscow Center of Fundamental and Applied Mathematics (agreement No. 075–15–2019–1624 with the Ministry of Education and Science of the Russian Federation).
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Transfer matrices and solution of the problem of stochastic dynamics of aerosol clusters by Monte Carlo method
- Constant upper bounds on the matrix exponential norm
- On the approximation of the diffusion operator in the ionosphere model with conserving the direction of geomagnetic field
- On numerical computation of sensitivity of response functions to system inputs in variational data assimilation problems
- Model reduction in Smoluchowski-type equations
Articles in the same Issue
- Frontmatter
- Transfer matrices and solution of the problem of stochastic dynamics of aerosol clusters by Monte Carlo method
- Constant upper bounds on the matrix exponential norm
- On the approximation of the diffusion operator in the ionosphere model with conserving the direction of geomagnetic field
- On numerical computation of sensitivity of response functions to system inputs in variational data assimilation problems
- Model reduction in Smoluchowski-type equations
