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ISSN Online: 2688-7231

ISBN Online: 978-1-56700-524-0

Proceedings of the 26thNational and 4th International ISHMT-ASTFE Heat and Mass Transfer Conference December 17-20, 2021, IIT Madras, Chennai-600036, Tamil Nadu, India
December, 17-20, 2021, IIT Madras, Chennai, India

Guidelines for type and order of quadrature in discrete ordinates method for radiative transfer in plane parallel medium

Get access DOI: 10.1615/IHMTC-2021.1680
pages 1107-1113

Abstract

Discrete ordinate method (DOM) is a widely used method for solving radiation transport equation (RTE) numerically. The present work focuses on a comprehensive assessment of DOM for a plain planar, absorbing, emitting and anisotropic scattering medium. In the initial part of the work, we show the heat transfer predictability using a standard eigen-value formulation along with angular discretizations handled by Gauss-Legendre Quadrature(GQ), Moment Matching method like Carlson and Lathrop Full Even Moment (CLFEM) as well as Half-Range Moment (CLHM) [13] and Fiveland's Half-Range Moment (FQ)[6]. In the subsequent part of the work, we have performed a systematic and extensive analysis to compare two angular discretizations quadrature schemes, GQ and FQ at radiative equilibrium, under black walls, optical thickness ranging from 0.1 to 10 and by taking 17 phase functions (PF) from literature. For optical thckness < 1, FQ is found to be better scheme for PF preferably less than 14 terms. Convergence when FQ is used deteriorates with increase in PF terms. For optical thckness > 1, GQ is found to be more effective than FQ for all PF. Dirac-Delta Phase function approximation is done to simplify highly scattering phase functions having many terms. This approximation has been used with both GQ and FQ. When used with GQ, the heat flux predictability is < 0.5% with less than 10 points for optical thickness > 2 and more number of points for optical thickness < 2. FQ gives heat flux predictability under 0.5% with less than 10 points for all optical thickness considered (0.1 to 10). The current work gives a good guideline for choice of type and order of quadrature when using DOM.
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