SPATIAL DIFFERENCING SCHEMES OF THE DISCRETE-ORDINATES METHOD

Abstract Several spatial differencing schemes are used to discretize the radiative transfer equation in the context of the discrete-ordinates method. These are the conventional upwind, central, hybrid, and exponential schemes as well as the high-resolution SMART scheme. The deferred correction strategy is adopted to incorporate the SMART scheme into the discrete-ordinates method. The TN quadrature set is used. Two nonscattering benchmark problems in two and three dimensions and one three-dimensional anisotropically scattering problem are considered. The radiation intensity is sensitive to the spatial differencing scheme used, while integral quantities are somewhat insensitive to the spatial differencing scheme. The SMART scheme yields accurate, nonoscillatory, and positive radiation intensity distributions. The central, exponential, and SMART schemes are almost equally accurate in the prediction of radiative heat transfer in both nonscattering and scattering media.

[1]  P. Gaskell,et al.  Curvature‐compensated convective transport: SMART, A new boundedness‐ preserving transport algorithm , 1988 .

[2]  M. Darwish,et al.  NORMALIZED VARIABLE AND SPACE FORMULATION METHODOLOGY FOR HIGH-RESOLUTION SCHEMES , 1994 .

[3]  J. P. Jessee,et al.  Comparison of discrete ordinates formulations for radiative heat transfer in multidimensional geometries , 1995 .

[4]  M. Pinar Mengüç,et al.  Radiation heat transfer in combustion systems , 1987 .

[5]  J. Truelove,et al.  Three-dimensional radiation in absorbing-emitting-scattering media using the discrete-ordinates approximation , 1988 .

[6]  Philip J. Smith,et al.  Predicting Radiative Transfer in Rectangular Enclosures Using the Discrete Ordinates Method , 1988 .

[7]  S. Patankar,et al.  Evaluation of spatial differencing practices for the discrete-ordinates method , 1994 .

[8]  Tae-Kuk Kim,et al.  Effect of anisotropic scattering on radiative heat transfer in two-dimensional rectangular enclosures , 1988 .

[9]  P. J. Smith,et al.  Three-dimensional discrete-ordinates modeling of radiative transfer in a geometrically complex furnace , 1993 .

[10]  B. P. Leonard,et al.  A stable and accurate convective modelling procedure based on quadratic upstream interpolation , 1990 .

[11]  Andrew Pollard,et al.  The TN Quadrature Set for the Discrete Ordinates Method , 1995 .

[12]  W. A. Fiveland,et al.  Three-dimensional radiative heat-transfer solutions by the discrete-ordinates method , 1988 .

[13]  K. D. Lathrop Spatial differencing of the transport equation: Positivity vs. accuracy , 1969 .

[14]  W. Fiveland Discrete-Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclosures , 1984 .