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-  2015 

稀疏网格与数论网格在饱和-非饱和流随机模拟中的应用与比较 Number net theory and sparse grid theory for stochastic modelling of saturated and unsaturated flow simulation

Keywords: 地下水,随机模型,稀疏网格法,数论网格法

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Abstract:

在饱和-非饱和流的随机模拟中,传统的蒙特卡罗方法收敛速度慢,计算成本高,特别是计算的误差为概率误差,易产生较大的不确定性.引入稀疏网格配点法和数论网格点集可以获得更好的模拟效果.通过算例分析和研究得出:在某些饱和-非饱和流随机模型的模拟中,稀疏网格配点法能够极大地节省计算成本,输出水头(或水质)具有确定的表达式,但是当随机变量维度较高或者模型中被积函数光滑性较差时,其模拟效果往往并不理想,甚至有可能出现违背物理现象的错误结果;数论网格法具有更好的适用性,维数越高,其优势越突出,且相比蒙特卡罗法精度要好,误差是确定的,避免了蒙特卡罗法概率误差带来的不确定性

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