Analog for monotone scheme for calculation of non self-conjugated system of quasi-diffusion equations in $r-z$-geometry

E. N. Aristova

Matematičeskoe modelirovanie, Tome 21 (2009) no. 2, pp. 47-59

Résumé

It is considered construction of a monotonous difference schemes analogue for not self-conjugated quasi-diffusion (QD) equations in $r-z$-geometry on an example of a non-stationary problem of external isotropic radiation propagation to a cylindrical pipe. For this purpose the coordinate rotation in a plane $(r,z)$ is done resulting diagonal form of QD tensor in the center of a cell, and, accordingly, it is achieved minimization of not diagonal elements on the sides of a cell. This scheme is similar to scheme offered for the self-conjugated problem [1]. The hybrid difference scheme is used in calculations which are nonmonotonic one in areas of decision smoothness and analogue of monotonous one at the nearest of contact boundaries. The perpendicularity of a front of light wave to the contact boundary makes a problem of external radiation propagation to a pipe to be the good test for research of a quality of the scheme.