Advances in the solution of three-dimensional nodal neutron transport equation

In this paper we study the three-dimensional nodal discrete-ordinates approximations of neutron transport equation in a convex domain with piecewise smooth boundaries. We use the combined collocation method of the angular variables and nodal approach for the spatial variables. By nodal approach we mean the iterated transverse integration of the SN equations. This procedure leads to the set of one-dimensional averages angular fluxes in each spatial variable. The resulting system of equations is solved with the LTSN method, first applying the Laplace transform to the set of the nodal SN equations and then obtaining the solution by symbolic computation. We include the LTSN method by diagonalization to solve the nodal neutron transport equation and then we outline the convergence of these nodal-LTSN approximations with the help of a norm associated to the quadrature formula used to approximate the integral term of the neutron transport equation. We give numerical results obtained with an algebraic computer system (for N up to 8) and with a code for higher values of N. We compare our results for the geometry of a box with a source in a vertex and a leakage zone in the opposite with others techniques used in this problem. (author)