Conjugacy Analysis of the Finite-Difference Equations of the Method of Characteristics on the Basis of a Linear-Algebraic Formulation

Abstract

A linear-algebraic form of the equations of the method of characteristics, which is used to approximate the neutron transport equation, is obtained. It is shown on the basis of the obtained linear-algebraic form that the discrete form of the conjugate equation differs from the algebraically discrete problem constructed by linear-algebraic transformations of the discrete form of the normal problem. The reason for the discrepancy lies in the approximation of the volumes of the spatial cells in covering the working region by a network of characteristics. It is shown by means of test calculations that when the network of characteristics is refined the solution of the conjugate transport equation converges to the solution of the algebraically conjugate problem.