Volume 4, Issue 1
Adaptive Stroud Stochastic Collocation Method for Flow in Random Porous Media via Karhunen-Loève Expansio

Yan Ding, Tiejun Li, Dongxiao Zhang & Pingwen Zhang

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Commun. Comput. Phys., 4 (2008), pp. 102-123.

Published online: 2008-04

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  • Abstract

In this paper we develop a Stochastic Collocation Method (SCM) for flow in randomly heterogeneous porous media. At first, the Karhunen-Loève expansion is taken to decompose the log transformed hydraulic conductivity field, which leads to a stochastic PDE that only depends on a finite number of i.i.d. Gaussian random variables. Based on the eigenvalue decay property and a rough error estimate of Stroud cubature in SCM, we propose to subdivide the leading dimensions in the integration space for random variables to increase the accuracy. We refer to this approach as adaptive Stroud SCM. One- and two-dimensional steady-state single phase flow examples are simulated with the new method, and comparisons are made with other stochastic methods, namely, the Monte Carlo method, the tensor product SCM, and the quasi-Monte Carlo SCM. The results indicate that the adaptive Stroud SCM is more efficient and the statistical moments of the hydraulic head can be more accurately estimated.

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@Article{CiCP-4-102, author = {}, title = {Adaptive Stroud Stochastic Collocation Method for Flow in Random Porous Media via Karhunen-Loève Expansio}, journal = {Communications in Computational Physics}, year = {2008}, volume = {4}, number = {1}, pages = {102--123}, abstract = {

In this paper we develop a Stochastic Collocation Method (SCM) for flow in randomly heterogeneous porous media. At first, the Karhunen-Loève expansion is taken to decompose the log transformed hydraulic conductivity field, which leads to a stochastic PDE that only depends on a finite number of i.i.d. Gaussian random variables. Based on the eigenvalue decay property and a rough error estimate of Stroud cubature in SCM, we propose to subdivide the leading dimensions in the integration space for random variables to increase the accuracy. We refer to this approach as adaptive Stroud SCM. One- and two-dimensional steady-state single phase flow examples are simulated with the new method, and comparisons are made with other stochastic methods, namely, the Monte Carlo method, the tensor product SCM, and the quasi-Monte Carlo SCM. The results indicate that the adaptive Stroud SCM is more efficient and the statistical moments of the hydraulic head can be more accurately estimated.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/10198.html} }
TY - JOUR T1 - Adaptive Stroud Stochastic Collocation Method for Flow in Random Porous Media via Karhunen-Loève Expansio JO - Communications in Computational Physics VL - 1 SP - 102 EP - 123 PY - 2008 DA - 2008/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/10198.html KW - AB -

In this paper we develop a Stochastic Collocation Method (SCM) for flow in randomly heterogeneous porous media. At first, the Karhunen-Loève expansion is taken to decompose the log transformed hydraulic conductivity field, which leads to a stochastic PDE that only depends on a finite number of i.i.d. Gaussian random variables. Based on the eigenvalue decay property and a rough error estimate of Stroud cubature in SCM, we propose to subdivide the leading dimensions in the integration space for random variables to increase the accuracy. We refer to this approach as adaptive Stroud SCM. One- and two-dimensional steady-state single phase flow examples are simulated with the new method, and comparisons are made with other stochastic methods, namely, the Monte Carlo method, the tensor product SCM, and the quasi-Monte Carlo SCM. The results indicate that the adaptive Stroud SCM is more efficient and the statistical moments of the hydraulic head can be more accurately estimated.

Yan Ding, Tiejun Li, Dongxiao Zhang & Pingwen Zhang. (2019). Adaptive Stroud Stochastic Collocation Method for Flow in Random Porous Media via Karhunen-Loève Expansio. Communications in Computational Physics. 4 (1). 102-123. doi:
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