On the approximation of the diffusion operator in the ionosphere model with conserving the direction of geomagnetic field

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.