Solution of the three‐dimensional transport equation using the spectral methods

Abstract

PurposeThe paper presents a method for solving the 3D steady state, linear transport equation in bounded domain.Design/methodology/approachThe method can be extended easily to general linear transport problem.FindingsThe idea of using the spectral method for searching solutions to the multi‐dimensional transport problems, leads us to a solution for all values of the independent variables.Research limitations/implicationsThe procedure is based on the development of the angular flux in a truncated series of Chebyshev polynomials in the spatial variables.Practical implicationsThe methodology used will permit us to transform the 3D problem into a set of 1D problems. The convergence of this approach is studied in the context of the discrete‐ordinates method.Originality/valueAn adaptation of this method for the convergence of the spectral solution within the framework of the analytical solution to study and prove convergence is relatively new.