Conditional Stochastic Simulations of Flow and Transport with Karhunen-Loève Expansions, Stochastic Collocation, and Sequential Gaussian Simulation
Conditional Stochastic Simulations of Flow and Transport with Karhunen-Loève Expansions, Stochastic Collocation, and Sequential Gaussian Simulation
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使用 Karhunen-Loève 展开式、随机搭配和顺序高斯模拟对流动和传输进行条件随机模拟
DOI：
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发表时间：
2014
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通讯作者：
V. Vasylkivska
中科院分区：
文献类型：
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作者：
M. Ossiander;M. Peszynska;V. Vasylkivska
我们推导了一种新的条件 Karhunen-Loeve (KL) 展开方法，用于地下流动和传输模型中的随机系数，特别是非均质随机渗透率场。该场的确切值永远未知，因此必须评估流动和传输模型解的不确定性。这通常是通过构建渗透率场的独立实现，然后对每个实现进行流动和传输的数值模拟，并组装所需感兴趣量的矩的统计估计来完成的。我们遵循众所周知的 KL 展开框架，并推导出一种新方法，该方法结合了给定位置的已知渗透率值，以便渗透率场的实现准确地遵循该数据。我们的方法依赖于对应用于协方差算子本征函数的随机权重的适当子空间的投影。我们在流动和传输模拟中使用通过随机模拟方法构建的渗透率实现，并将结果与通过顺序高斯模拟 (SGS) 构建实现时获得的结果进行比较。我们还将效率和随机收敛与随机配置的效率和随机收敛进行了比较。
We derive a new method of conditional Karhunen-Loeve (KL) expansions for stochastic coefficients in models of flow and transport in the subsurface, and in particular for the heterogeneous random permeability field. Exact values of this field are never known, and thus one must evaluate uncertainty of solutions to the flow and transport models. This is typically done by constructing independent realizations of the permeability field followed by numerical simulations of flow and transport for each realization and assembling statistical estimates of moments of desired quantities of interest. We follow the well-known framework of KL expansions and derive a new method that incorporates known values of the permeability at given locations so that the realizations of the permeability field honor this data exactly. Our method relies on projections to an appropriate subspace of random weights applied to the eigenfunctions of the covariance operator. We use the permeability realizations constructed with our stochastic simulation method in simulations of flow and transport and compare the results to those obtained when realizations are constructed with sequential Gaussian simulation (SGS). We also compare efficiency and stochastic convergence with that of stochastic collocation.