APPLICATION OF THE TVD-APPROACH TO THE DSn-METHOD FOR THE HEAT RADIATION TRANSPORT EQUATION SOLUTION IN THE AXIALLY-SYMMETRIC RZ-GEOMETRY
A. D. Gadzhiev, V. V. Zavyalov, A. A. Shestakov
VANT. Ser.: Mat. Mod. Fiz. Proc 2010. Вып.2. С. 30-39.
Realization of the implicit nonlinear TVD-type scheme of a higher approximation order is considered for the solution of the heat radiation transport equation in the axially-symmetrical RZ-geometry on arbitrary quadrangular grids in the frames of the discrete ordinates. A limiter is used in the scheme, which is calculated explicitly over the values known from the previous time step on a three-point template in each direction. This property allows application of the time-saving sweep computation for the solution of the system of difference equations. The scheme combines conservativeness, smoothness in the sense of the TVD-scheme methodology, first order approximation over time and second order approximation over space, except several points with extremums. The order of approximation is studied for a model transport equation. Earlier this scheme was tested for 1D geometries. The results of test problem numerical calculations are presented.Keywords: radiation transport, difference scheme, method of discrete ordinates, TVD approach.
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