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離散坐標法積分方案的選取

Selection of Angular Quadrature Schemes for Discrete Ordinate Method

  • 摘要: 以輻射平衡條件下一維平行平板介質層的輻射換熱問題為例,介紹了求解輻射傳遞方程的離散坐標法,對影響離散坐標法計算精度與速度的角度積分方案的選取進行了研究.分析了離散坐標法常用的SN積分方案、Fiveland等權值積分方案FN及高斯積分方案GN對計算結果準確性的影響.研究表明:積分方案近似階數越高,計算結果的精度越高,但隨著積分方案階數的增加,所需的計算量也增大;同一近似階數的各種積分方案的準確性各不相同,其中FN積分方案在相同階數下的精度最高,SN積分方案次之,GN積分方案的精度最差.在近似階數足夠高時上述三種積分方案均可達到較高的計算精度.

     

    Abstract: 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.

     

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