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首页> 外文期刊>Advances in Water Resources >An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media
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An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media

机译：稀疏网格上随机异质多孔介质中三维流动和溶质运移的高效高阶概率配置方法

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摘要

In this study, a probabilistic collocation method (PCM) on sparse grids is used to solve stochastic equations describing flow and transport in three-dimensional, saturated, randomly heterogeneous porous media. The Karhunen-Loeve decomposition is used to represent log hydraulic conductivity Y = InK_s. The hydraulic head h and average pore-velocity v are obtained by solving the continuity equation coupled with Darcy's law with random hydraulic conductivity field. The concentration is computed by solving a stochastic advection-dispersion equation with stochastic average pore-velocity v computed from Darcy's law. The PCM approach is an extension of the generalized polynomial chaos (gPC) that couples gPC with probabilistic collocation. By using sparse grid points in sample space rather than standard grids based on full tensor products, the PCM approach becomes much more efficient when applied to random processes with a large number of random dimensions. Monte Carlo (MC) simulations have also been conducted to verify accuracy of the PCM approach and to demonstrate that the PCM approach is computationally more efficient than MC simulations. The numerical examples demonstrate that the PCM approach on sparse grids can efficiently simulate solute transport in randomly heterogeneous porous media with large variances.
机译：在这项研究中，使用稀疏网格上的概率配置方法（PCM）来求解描述在三维，饱和，随机非均质多孔介质中的流动和传输的随机方程。 Karhunen-Loeve分解用于表示对数水力传导率Y = InK_s。通过求解连续方程，结合达西定律和随机水力传导率场，获得水力头h和平均孔隙速度v。通过求解具有由达西定律计算的随机平均孔隙速度v的随机对流扩散方程来计算浓度。 PCM方法是广义多项式混沌（gPC）的扩展，它将gPC与概率搭配耦合在一起。通过在样本空间中使用稀疏网格点而不是基于全张量积的标准网格，当将PCM方法应用于具有大量随机尺寸的随机过程时，PCM方法变得更加高效。还进行了蒙特卡洛（MC）仿真，以验证PCM方法的准确性，并证明PCM方法在计算上比MC仿真更有效。数值算例表明，稀疏网格上的PCM方法可以有效地模拟溶质在随机变异性较大的多孔介质中的运移。

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