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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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SOME METHODS OF APPROXIMATION FOR 2D TRANSPORT EQUATION BY ANGLE VARIABLES
R. M. Shagaliev, A. V. Alekseev, S. V. Mzhachikh, N. P. Pleteneva VANT. Ser.: Mat. Mod. Fiz. Proc. 2003. Вып.2. С. 511.
Traditional S_{n} techniques of angle variable discretization of phase space are known to require a refined angle grid. Otherwise a radiation effect, as it is called, may occur. More stringent requirements to the number of angular variable intervals may result in essentially growing consumption of CP time and PC online storage for computations. One of the resolutions of this issue may be that of developing more efficient methods of multidimensional transport equation solution in angular variables. The following four approximation schemes for the transport equation in angular variables are under consideration: a traditional method for solving 2D transport equation using DS_{n} schemes; an improved scheme, meeting such requirements as exact calculation of “moment” integrals and diffusion limit obtaining; two variants of WDD scheme, in which an output flow through faces of a phase cell is recalculated.
 NUMERICAL STUDY RESULTS FOR VARIOUS METHODS OF 2D TRANSPORT EQUATION APPROXIMATION IN ANGLE VARIABLES
R. M. Shagaliev, A. V. Alekseev, O. E. Vlasova, V. V. Evdokimov, A. V. Gichuk, E. A. Irinichev, S. V. Mzhachikh, A. A. Nuzhdin, N. P. Pleteneva, H. Scott VANT. Ser.: Mat. Mod. Fiz. Proc. 2003. Вып.2. С. 1220.
The paper presents numerical study results for some updated methods of solving 2D radiative transport equation in angular variables. The methods have been described in the previous paper on this line. Several model problems of radiation propagation were numerically studied. The results are discussed in terms of grid solution accuracy. The conclusions are drawn regarding the efficiency of the methods used for the class of problems under consideration.

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