积分格式对窄带k-分布计算的影响

Impact of integral scheme on narrow-band k-distribution

对于窄带k-分布模型,影响计算精度的关键因素是积分格式,为了研究积分格式对窄带k-分布模型的影响,选择了5种精度较高的高斯积分方法进行计算分析。首先采用Gauss-Lobatto7点积分格式窄带k-分布法计算了CO2四种条件下的窄带平均透过率,并与实验结果进行对比验证,对比结果吻合良好。另外选取了4种积分方式:Gauss-Lobatto5、Gauss-Lobatto4、Gauss-Legendre 4和Gauss-Legendre2点积分,对CO2的四个算例进行计算,并将5种积分格式的计算结果与逐线计算结果进行对比分析。结果表明:Gauss-Lobatto7的精度最高,Gauss-Lobatto5和Gauss-Legendre4次之,其中Gauss-Legendre4略高于Gauss-Lobatto 5。显然相同积分方法积分点越多计算精度越高,但计算时间越长,而两种不同积分方法对比Gauss-Legendre优于Gauss-Lobatto。综合考虑精度与计算时间等因素,5种积分格式中Gausslegendre 4应该为最好的选择。

One of the key factors for narrow-band k-distribution model is integral scheme, for studying of the impact of integral scheme on narrow-band k-distribution model, five high-accuracy Gaussian integral schemes were studied. The narrow-band average transmissivity data of CO2 for four different conditions were calculated by narrow-band k-distribution of Gauss-Lobatto 7, and the comparison results were in good agreement with those of testing ones. In addition, Four new integral schemes, Gauss-Lobatto 5, Gauss-Lobatto 4, Gauss-Legendre 4 and Gauss-Legendre 2, were used to calculate four cases of CO2, and the comparsions of the results calculated by the five integral schemes with the line by line ones were discussed. The results indicate that the accuracy of Gauss-Lobatto 7 is the highest, next are Gauss-Lobatto 5 and Gauss-Legendre 4, that is higher than Gauss-Legendre 5. Obviously, for the same scheme, the more the number of integral point, the higher the calculation precision and the longer the calculation time, but for two different schemes, Gauss-Legendre is better than Gauss-Lobatto. Considered comprehensively, Gauss-Legendre 4 is better than others.