采用蒙特卡罗法分析离散坐标法的假散射

Analyses of the false scattering of the Discrete Ordinates method by using Monte Carlo method

采用蒙特卡罗法获得了离散坐标方程的不含任何假散射的高精度解 ,其基本思路是 :当采用一个离散坐标格式来计算一个漫射表面的热辐射时 ,就意味着用有限个离散方向去“代表”2π立体空间上的无穷多个方向 .因此 ,不妨假定存在着这样一个虚拟表面 :该表面的确只沿着该离散坐标格式的离散方向上发射热辐射 ,并且在每个方向上的热流也完全遵循离散坐标方程 .然后将蒙特卡罗法应用于此虚拟表面 ,由此所获得的解即为此虚拟表面的高精度解 ,不言而喻它也等效于离散坐标方程的高精度解 .在此基础上 。

The precise solutions to the discrete ordinate equations are obtained by using Monte Carlo Method. When a discrete ordinate quadrate set is employed to calculate the thermal radiation of a diffuse surface, the infinite number of directions in the solid angle 2π are 'represented' by a finite number of discrete directions. Monte Carlo method is employed to calculate the thermal radiation of this fictitious surface. The corresponding solutions are the precise solutions of this fictitious surface, and also equivalent to the precise solutions of the discrete ordinate equations. Based on the precise solutions, the effect of the false scattering associated with the Discrete Ordinate Method on the computational results is analyzed.