Global Random Walk Solutions for Flow and Transport in Porous Media
Global Random Walk Solutions for Flow and Transport in Porous Media
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多孔介质中流动和传输的全局随机游走解决方案
DOI：
10.1007/978-3-030-55874-1_93
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发表时间：
2019
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本文提出了一种利用规则网格上的随机游动求解非均质多孔介质中渗流方程的新方法。水头由计算粒子表示，这些粒子根据随机游走规则从网格点全局分布，跳跃概率由水力传导系数确定。后者被建模为作为周期性随机模式的叠加生成的随机函数的实现。一维和二维数值解与分析制造的解决方案进行了比较验证。此外，与新的方法计算的无发散速度场的系综被用来进行随机场中的扩散的Monte Carlo模拟。输运方程通过全局随机游走算法求解，该算法将代表溶质浓度的计算粒子移动到与用于求解流动方程的相同的晶格上。综合流动和运输解决方案验证了一个很好的协议之间的统计估计的前两个空间时刻的溶质羽流和随机理论的预测在地下水中的运输。
This article presents a new approach to solve the equations of flow in heterogeneous porous media by using random walks on regular lattices. The hydraulic head is represented by computational particles which are spread globally from the lattice sites according to random walk rules, with jump probabilities determined by the hydraulic conductivity. The latter is modeled as a realization of a random function generated as a superposition of periodic random modes. One- and two-dimensional numerical solutions are validated by comparisons with analytical manufactured solutions. Further, an ensemble of divergence-free velocity fields computed with the new approach is used to conduct Monte Carlo simulations of diffusion in random fields. The transport equation is solved by a global random walk algorithm which moves computational particles representing the concentration of the solute on the same lattice as that used to solve the flow equations. The integrated flow and transport solution is validated by a good agreement between the statistical estimations of the first two spatial moments of the solute plume and the predictions of the stochastic theory of transport in groundwater.
随机场中的扩散
DOI：
10.1007/978-3-030-15081-5
发表时间：
2019
期刊：
Geosystems Mathematics
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