Application of the statistical narrow-band correlated-k method to low-resolution spectral intensity and radiative heat transfer calculations — effects of the quadrature scheme

The statistical narrow-band correlated-k method was employed to calculate low-resolution spectral intensity along a line-of-sight, and radiative heat transfer in both, a one-dimensional parallel-plates enclosure and a three-dimensional rectangular enclosure containing CO2–H2O–N2 mixtures under various conditions. Numerical calculations were conducted using six quadrature schemes: the commonly used “7-point Gauss–Lobatto” quadrature, the 4-point, 2-point, and 1-point Gauss–Legendre quadratures, and the 4-point and 5-point Gauss–Lobatto quadratures. The “7-point Gauss–Lobatto” quadrature yields very accurate results compared to the results of the statistical narrow-band model. Results of the 4-point Gauss–Legendre quadrature are only slightly less accurate than those of the “7-point Gauss–Lobatto” quadrature. The 2-point Gauss–Legendre quadrature offers acceptably good accuracy with much less computing efforts, especially for calculations of spectrally integrated quantities. Results of the 1-point Gauss–Legendre are in serious error. The overall performance of the 4-point and 5-point Gauss–Lobatto quadratures is even worse than that of the 2-point Gauss–Legendre quadrature.