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

Abstract

Purpose

The paper presents a method for solving the 3D steady state, linear transport equation in bounded domain.

Design/methodology/approach

The method can be extended easily to general linear transport problem.

Findings

The 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/implications

The procedure is based on the development of the angular flux in a truncated series of Chebyshev polynomials in the spatial variables.

Practical implications

The 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/value

An 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.

Citation

Kadem, A. (2007), "Solution of the three‐dimensional transport equation using the spectral methods", Kybernetes, Vol. 36 No. 2, pp. 236-252. https://doi.org/10.1108/03684920710741242