Journal of Physical Studies 2(3), 427–432 (1998) DOI: https://doi.org/10.30970/jps.02.427 THE PROBLEM OF TWO-DIMENSIONAL RADIATIVE TRANSFER FOR MULTILEVEL ATOMS

M. Stodilka, R. Rykaliuk
The Ivan Franko State University of Lviv, Computer Center,
1 University Str., UA–290005, Lviv, Ukraine

The present paper deals with detailed analyses of radiative transfer and statistical equilibrium equations solution problem. The problem is solved by using multigrid techniques. This approach guarantees convergence to true solution since long periodical oscillations of the solution are being filtered, and the convergence itself becomes essentially improved. On each grid the solution is found by the accelerated $Λ$–iteration method. For the formal solution of the radiative transfer equation the short characteristics method is used. The method under the linear interpolation of source function gives a simple recurrent relationship for the radiation intensity which is spread in a given direction. For the statistical equilibrium equations the preconditioning procedure is used. Such a procedure ensures positive solutions and the equations themselves linearly depend on level populations which results in linear convergence. The ways of linear convergence improvement are described. Using the short characteristics approach the coefficients for local and quasilocal approximate $Λ$–operators have been obtained. In the latter the nearest neighbouring points conditions have been taken into account and that improves the operator quality.

Described techniques allow to study inhomogeneous astrophysical plasma.

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