Specular reflection treatment for the 3D radiative transfer equation solved with the discrete ordinates method

Journal Article · Sat Apr 01 04:00:00 EDT 2017 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2017.01.019· OSTI ID:22622276

Le Hardy, D. ^[1]; Rousseau, B. ^[1]; Hecht, F. ^[2]

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1. Université de Nantes, LTN UMR CNRS 6607 (France)
2. Sorbonne Universités, UPMC Université Paris 06, UMR 7598, inria de Paris, Laboratoire Jacques-Louis Lions, F-75005, Paris (France)

The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken into account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.

• OSTI ID: 22622276
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 334; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ALGORITHMS
ANALYTICAL SOLUTION
COMPARATIVE EVALUATIONS
COMPUTER CALCULATIONS
DISCRETE ORDINATE METHOD
EQUATIONS
FINITE ELEMENT METHOD
PARTITION
QUADRATURES
RADIANT HEAT TRANSFER
REFLECTION