离散坐标法积分方案的选取

Selection of Angular Quadrature Schemes for Discrete Ordinate Method

以辐射平衡条件下一维平行平板介质层的辐射换热问题为例,介绍了求解辐射传递方程的离散坐标法,对影响离散坐标法计算精度与速度的角度积分方案的选取进行了研究.分析了离散坐标法常用的S_N积分方案、Fiveland等权值积分方案F_N及高斯积分方案G_N对计算结果准确性的影响.研究表明:积分方案近似阶数越高,计算结果的精度越高,但随着积分方案阶数的增加,所需的计算量也增大;同一近似阶数的各种积分方案的准确性各不相同,其中F_N积分方案在相同阶数下的精度最高,S_N积分方案次之,G_N积分方案的精度最差.在近似阶数足够高时上述三种积分方案均可达到较高的计算精度.

The radiative heat transfer of one-dimensional plane-parallel slabs under radiative equilibrium was investigated by Discrete Ordinate Method (DOM): The selection of angular quadrature schemes, which is very important to the accuracy and calculation time of DOM, was studied. The accuracy of the SN approximation quadrature scheme, Fiveland's angular quadrature scheme with equal weights FN and Gauss angular quadrature scheme GN was analyzed. It shows that the accuracy and computation time of DOM increases with the increase of the order of each quadrature scheme. The accuracy of DOM is different from each other for the three quadrature schemes with the same order and FN is the best one among them. As a conclusion, FN is recommended in DOM calculations.