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QUASI-DIFFUSION METHOD APPLICATION TO SOLVE 2D AXIALLY-SYMMETRIC PROBLEMS OF RADIATION TRANSPORT IN SPECTRAL-KINETIC SCENARIO USING A SQUARE GRID

N. G. Karlykhanov, A. V. Urakova, S. A. Shnitko
VANT. Ser.: Mat. Mod. Fiz. Proc 2011. Вып.2. С. 33-43.

The paper considers an implicit scheme used to solve the radiation transport equation in quasi-diffusion approximation along with the energy equation in a 2D case using a square grid. For the transport equation we use a conservative monotone difference scheme of the first accuracy order. Since it is a well-known fact that there are no linear, monotone, difference schemes of the second accuracy order for hyperbolic equation systems, we propose a hybrid difference scheme to solve the quasi-diffusion type equations. It is a combination of schemes of the first and second orders of accuracy and provides the monotone behavior of solution. The method of singling out a diagonal element is used to solve quasi-diffusion equations along with the energy equation.

Keywords: radiation transport equation, quasi-diffusion equations, equation of energy.








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