PROBABILISTIC METHOD OF DISCRETE ORDINATES IN A NEUTRON-TRANSPORT PROBLEM

A new numerical method, the probabilistic method of discrete ordinates (PMDO) for solving multigroup transport equations in three-dimensiona l complex geometry, is presented. The method can be used for reactor c ore and shielding calculations. Integral equations are adopted for The angular flux in cells of arbitrary for m. They are coupled by means o f net currents defined at interfaces. The sphere of directions is arbi trarily subdivided into a number of angular diapasons. These diapasons , along with cell volume and pieces of cell surface, produce elementar y phase domains, so the basic PMDO equations are the algebraic analogu es of piecewise coupled integral transport equations. They are written for neutron flux and currents integrated over corresponding phase dom ains. The coefficients of the equations discretely depend on the angul ar variable and have the meaning of probabilities of uncollided neutro ns being transmitted between different phase domains. On the basis of algebraic equations separately obtained for coarse and fine domains, t he global-local iterative PMDO scheme has also been developed specific ally for calculations in extensive heterogeneous media. Together with the direct PMDO equations, the system of conjugate equations has been constructed for the calculation of neutron importance function related to various nonlinear functionals. Codes based on the method and some numerical applications, including examples related to criticality calc ulations and deep penetration problems, have been briefly discribed.