Acceleration of the numerical solution for the radiative transfer equation using a modified relaxation factor: X-factor method. Issue 5 (29th January 2020)

• Record Type: Journal Article
• Authors: Torres-Aguilar, Carlos Enrique; Xamán, Jesús; Moreno-Bernal, Pedro; Hernández-Pérez, Iván; Zavala-Guillén, Ivett; Hernández-López, Irving Osiris
• Is Part Of: Engineering computations. Volume 37:Issue 5(2020)
• Page Start: 1823
• Page End: 1847
• Publication Date: 2020-01-29
• Subjects: Deferred-correction -- High-resolution TVD schemes -- Radiative transfer equation; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-05-2019-0210
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: The purpose of this study is to propose a novel relaxation modified factor to accelerate the numerical solution of the radiative transfer equation (RTE) with several high-resolution total variation diminishing schemes. The methodology proposed is denoted as the X-factor method. Design/methodology/approach: The X-factor method was compared with the technique deferred-correction (DC) for the calculations of a two-dimensional cavity with absorting-emiting-scatteting gray media using the discrete ordinates method. Four parameters were considered to evaluate: the absorption coefficient, the emissivity of boundary surface, the scattering albedo and under-relaxation factor. Findings: The results showed the central processing unit (CPU) time of X-factor method was lower than DC. The reductions of CPU time with the X-factor method were observed from 0.6 to 75.4%. Originality/value: The superiority of the X-factor method over DC was showed with the reduction of CPU time of the numerical solution of RTE for evaluated cases.