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

Journal Article · Wed Jun 01 00:00:00 EDT 2011 · Journal of Computational Physics

OSTI ID:21499749

Xiang, Ma ^[1]; Zabaras, Nicholas ^[1]

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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)

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.

• OSTI ID: 21499749
• Journal Information: Journal of Computational Physics, Vol. 230, 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.; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

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