Analog of the monotone scheme to solve the non-self-conjugated set of quasi-diffusion equations in r–z geometry

Abstract

The way to generate the monotonous difference scheme similar to non-self-conjugated quasi-diffusion equations in r–z geometry is examined through an example of a nonstationary problem of external isotropic radiation propagation in a cylindrical pipe. For this purpose, the coordinates in a plane (r, z) are rotated in such a way that the quasi-diffusion tensor takes a diagonal form in the center of the cell and, therefore, the nondiagonal elements on the side of the cell are minimized. This scheme is similar to the scheme that we have already developed for a self-conjugated problem [1]. The following hybrid difference scheme is used in calculations: it is non-monotone in the areas of smooth solutions and is analog to monotone at the contact boundaries. Note that for the plane case the non-monotone difference scheme is invariant relative to the rotation of the coordinates. Since the front of the light wave is normal to the contact boundary, the problem of the penetration of the external radiation in the pipe is useful in verifying the quality of the scheme