Abstract
A finite analytic (not finite-difference) scheme is derived for the numerical solution of evenand odd-parity transport equations of neutral particles. This discrete algebraic equation is constructed by cross-linking analytic solutions of differential equations in tetrahedral cells. Such a scheme makes it possible to simulate the three-dimensional transport of neutrons and photons in heterogeneous absorbing, scattering, and multiplying media (simulate problems of nuclear reactors, radiation shielding, radiative heat exchange, and radiation gas dynamics) without restrictions on the optical depth of the cell (the product of the beam extinction coefficient by the cell chord) and on the value of the jump in the extinction coefficient under the particle transition from one cell to another. A change in the sign of the extinction coefficient is allowed. The scheme is combined with efficient iterative methods for solving deterministic transport problems in which the angular (direction-of-flight) variable is discretized using the discrete-ordinate (Sn) approximation.
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