Efficient Stochastic Finite Element Methods for Flow in Heterogeneous Porous Media. Part 2: Random Lognormal Permeability,International Journal for Numerical Methods in Fluids

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Efficient Stochastic Finite Element Methods for Flow in Heterogeneous Porous Media. Part 2: Random Lognormal Permeability
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2020-04-27 , DOI: 10.1002/fld.4842
Luca Traverso _{1,

2} , Timothy Nigel Phillips ₂

Affiliation

Efficient and robust iterative methods are developed for solving the linear systems of equations arising from stochastic finite element methods for single phase fluid flow in porous media. Permeability is assumed to vary randomly in space according to some given correlation function. In the companion paper, herein referred to as Part 1, permeability was approximated using a truncated Karhunen‐Loeve expansion (KLE). The stochastic variability of permeability is modeled using lognormal random fields and the truncated KLE is projected onto a polynomial chaos basis. This results in a stochastic nonlinear problem since the random fields are represented using polynomial chaos containing terms that are generally nonlinear in the random variables. Symmetric block Gauss‐Seidel used as a preconditioner for CG is shown to be efficient and robust for stochastic finite element method.

中文翻译：

非均质多孔介质中流动的有效随机有限元方法。第 2 部分：随机对数正态渗透率

开发了高效且稳健的迭代方法，用于求解由多孔介质中单相流体流动的随机有限元方法产生的线性方程组。根据某些给定的相关函数，假设渗透率在空间中随机变化。在本文中称为第 1 部分的配套论文中，使用截断的 Karhunen-Loeve 展开 (KLE) 来近似渗透率。渗透率的随机变化使用对数正态随机场建模，截断的 KLE 投影到多项式混沌基础上。这会导致随机非线性问题，因为随机场使用多项式混沌表示，其中包含随机变量中通常为非线性的项。

更新日期：2020-04-27

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