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Title: A stochastic mixed finite element heterogeneous multiscale method for flow in porous media

Abstract

A computational methodology is developed to efficiently perform uncertainty quantification for fluid transport in porous media in the presence of both stochastic permeability and multiple scales. In order to capture the small scale heterogeneity, a new mixed multiscale finite element method is developed within the framework of the heterogeneous multiscale method (HMM) in the spatial domain. This new method ensures both local and global mass conservation. Starting from a specified covariance function, the stochastic log-permeability is discretized in the stochastic space using a truncated Karhunen-Loeve expansion with several random variables. Due to the small correlation length of the covariance function, this often results in a high stochastic dimensionality. Therefore, a newly developed adaptive high dimensional stochastic model representation technique (HDMR) is used in the stochastic space. This results in a set of low stochastic dimensional subproblems which are efficiently solved using the adaptive sparse grid collocation method (ASGC). Numerical examples are presented for both deterministic and stochastic permeability to show the accuracy and efficiency of the developed stochastic multiscale method.

Authors:
 [1];  [1]
  1. Materials Process Design and Control Laboratory, Sibley School of Mechanical and Aerospace Engineering, 101 Frank H.T. Rhodes Hall, Cornell University, Ithaca, NY 14853-3801 (United States)
Publication Date:
OSTI Identifier:
21499749
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 230; Journal Issue: 12; Other Information: DOI: 10.1016/j.jcp.2011.03.001; PII: S0021-9991(11)00131-8; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ACCURACY; FINITE ELEMENT METHOD; FUNCTIONS; MATHEMATICAL SPACE; PARTIAL DIFFERENTIAL EQUATIONS; PERMEABILITY; POROUS MATERIALS; RANDOMNESS; STOCHASTIC PROCESSES; TRANSPORT THEORY; CALCULATION METHODS; DIFFERENTIAL EQUATIONS; EQUATIONS; MATERIALS; MATHEMATICAL SOLUTIONS; NUMERICAL SOLUTION; PHYSICAL PROPERTIES; SPACE

Citation Formats

Xiang, Ma, and Zabaras, Nicholas. A stochastic mixed finite element heterogeneous multiscale method for flow in porous media. United States: N. p., 2011. Web.
Xiang, Ma, & Zabaras, Nicholas. A stochastic mixed finite element heterogeneous multiscale method for flow in porous media. United States.
Xiang, Ma, and Zabaras, Nicholas. Wed . "A stochastic mixed finite element heterogeneous multiscale method for flow in porous media". United States.
@article{osti_21499749,
title = {A stochastic mixed finite element heterogeneous multiscale method for flow in porous media},
author = {Xiang, Ma and Zabaras, Nicholas},
abstractNote = {A computational methodology is developed to efficiently perform uncertainty quantification for fluid transport in porous media in the presence of both stochastic permeability and multiple scales. In order to capture the small scale heterogeneity, a new mixed multiscale finite element method is developed within the framework of the heterogeneous multiscale method (HMM) in the spatial domain. This new method ensures both local and global mass conservation. Starting from a specified covariance function, the stochastic log-permeability is discretized in the stochastic space using a truncated Karhunen-Loeve expansion with several random variables. Due to the small correlation length of the covariance function, this often results in a high stochastic dimensionality. Therefore, a newly developed adaptive high dimensional stochastic model representation technique (HDMR) is used in the stochastic space. This results in a set of low stochastic dimensional subproblems which are efficiently solved using the adaptive sparse grid collocation method (ASGC). Numerical examples are presented for both deterministic and stochastic permeability to show the accuracy and efficiency of the developed stochastic multiscale method.},
doi = {},
url = {https://www.osti.gov/biblio/21499749}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = 12,
volume = 230,
place = {United States},
year = {2011},
month = {6}
}