Comparison of three discrete ordinates methods applied to two-dimensional curved geometries

• Published in: International journal of thermal sciences Vol. 42; no. 4; pp. 343 - 359
• Main Authors: Koo, Hong-Mo, Vaillon, Rodolphe, Goutière, Vincent, Le Dez, Vital, Cha, Hojin, Song, Tae-Ho
• Format: Journal Article
• Language: English
• Published: Paris Elsevier Masson SAS 01.04.2003; Elsevier
• Subjects: Analytical and numerical techniques; Curved geometry; Discrete ordinates; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Heat transfer; Mechanics; Physics; Radiation; Radiative equilibrium; Reflecting wall; Structured and unstructured grids; Thermal radiation; Thermics; Curved geometry; Discrete ordinates; Structured and unstructured grids; Reflecting wall; Radiation; Radiative equilibrium; Thermal radiation; Thermal emissivity; Gray medium; Digital simulation; Heat flow; Curved surface; Radiative transfer; Mesh generation; Discrete ordinate method; Reflecting surface
• ISSN: 1290-0729; 1778-4166
• DOI: 10.1016/S1290-0729(02)00036-4

This paper describes the application and comparison of three Discrete Ordinates Methods: the Discrete Ordinates Interpolation Method (DOIM) for structured and unstructured grids; the Discrete Ordinates Method in Orthogonal Curvilinear Coordinates (DOM-OCC) for structured grid; and the Discrete Ordinates Method associated to the Finite Volume method and Ray Tracing (DOM-FV-RT) for unstructured grid. A summary of the basic equations and numerical formulations is given for each method to outline their key characteristics. In order to extract valuable information to improve DO kind methods when applied to complex geometries, they are compared in the case of radiative equilibrium of a gray medium confined between infinite black or diffusely reflecting circular or elliptical cylinders. For the circular ring problem, the three DOMs results are confronted with Monte Carlo ones for various radius ratios and radiative properties. The elliptical ring problem extends the comparison to a more complex geometry and an emphasis is put on the evaluation of wall radiation fluxes. In conclusion, distinctive features in terms of performances are observed for each method.