A Positive Scheme for the Radiation Transport Equation in Greatly Heterogeneous Media and Voids. Parts 1-2

A new method of weights choice in the known weighted WDD scheme of the discrete ordinate method for the radiation transport equation in cylindrical (r,z)-geometry is proposed. In each cell of spatial grid for each node of angular quadrature weights are chosen so that solution (angular distribution), obtained by balance WDD scheme, possesses good (quantitative and qualitative) properties of solution, obtained by nonconservative characteristics scheme. The method may be extended in other geometry.