格林函数时间卷积法在输运求解中的应用

Study of Using Green Function Integral to Solve Transportation Problem

摘要: 利用瞬时源的格林函数卷积，可求解具有一定时间分布源粒子的输运问题。首先从输运方程的一般形式推导得到了格林函数时间卷积法的公式，并结合蒙特卡罗数值模拟算例，验证了格林函数时间卷积法在定态含时输运问题中的适用性，为相关问题的求解提供了新的思路。进一步数值分析表明，对于某些实际模型的蒙特卡罗求解，在同样计算样本条件下，格林函数卷积法还能实现较高的计算精度。

Abstract: The transportation problem with time-dependent source could be solved by the Green function integral method. The method was deducted from the common transportation function and demonstrated with some Monte Carlo numerical simulation test. The method provides a new way to solve the related problem. The further analysis for numerical simulation result shows that the calculation statistical error can be reduced by the Green function integral method with same calculate condition.