APPLICATION OF THE TVDAPPROACH TO THE DS_{n}METHOD FOR THE HEAT RADIATION TRANSPORT EQUATION SOLUTION IN THE AXIALLYSYMMETRIC RZGEOMETRY
A. D. Gadzhiev, V. V. Zavyalov, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc 2010. Вып.2. С. 3039.
Realization of the implicit nonlinear TVDtype scheme of a higher approximation order is considered for the solution of the heat radiation transport equation in the axiallysymmetrical RZgeometry 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 threepoint template in each direction. This property allows application of the timesaving sweep computation for the solution of the system of difference equations. The scheme combines conservativeness, smoothness in the sense of the TVDscheme 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.
