Analysis of stochastic mimetic finite difference methods and their applications in single-phase stochastic flows
Analysis of stochastic mimetic finite difference methods and their applications in single-phase stochastic flows
复制标题
DOI：
10.1016/j.cma.2011.12.007
复制
发表时间：
2012-04
影响因子：
7.2
通讯作者：
Lijian Jiang;J. Moulton;D. Svyatskiy
中科院分区：
文献类型：
--
作者：
Lijian Jiang;J. Moulton;D. Svyatskiy
随机建模已成为一种广泛接受的方法，用于量化扩散发挥核心作用的应用中的不确定性。在许多此类应用中，几何形状很复杂，需要准确捕获底层确定性连续体模型的重要属性。为了解决这些问题，我们提出了一种用于具有随机输入数据的扩散方程的随机模拟有限差分（MFD）方法。具体来说，我们使用 MFD 方法进行空间近似，以确保实现必要的准确性和鲁棒性。为了有效地处理随机近似的高维性，我们使用随机配置方法。我们考虑混合形式的随机 MFD 近似，并对压力、通量和拉格朗日乘子的半离散化和全离散化进行严格分析。收敛率是针对感兴趣数量的统计矩而开发的。给出了随机多孔介质中单相流的数值结果，并支持随机 MFD 的效率。
Stochastic modeling has become a widely accepted approach to quantify uncertainty in applications where diffusion plays a central role. In many of these applications the geometry is complex, and important properties of the underlying deterministic continuum model need to be captured accurately. To address these problems we present a stochastic mimetic finite difference (MFD) method for diffusion equations with random input data. Specifically, we use the MFD methodology for the spatial approximation to ensure the necessary accuracy and robustness is achieved. To treat the high-dimensionality of the stochastic approximation efficiently, we use a stochastic collocation method. We consider the stochastic MFD approximation in hybrid form, and perform a rigorous analysis of its semi-discretization and full discretization for the pressure, flux and Lagrange multipliers. Convergence rates are developed for statistical moments of the quantities of interest. Numerical results are presented for single-phase flow in random porous media, and support the efficiency of the stochastic MFD.