A stochastic multiscale framework for modeling flow through random heterogeneous porous media

Journal Article · Sun Feb 01 04:00:00 EST 2009 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2008.10.006· OSTI ID:21167747

Ganapathysubramanian, B ^[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)

Flow through porous media is ubiquitous, occurring from large geological scales down to the microscopic scales. Several critical engineering phenomena like contaminant spread, nuclear waste disposal and oil recovery rely on accurate analysis and prediction of these multiscale phenomena. Such analysis is complicated by inherent uncertainties as well as the limited information available to characterize the system. Any realistic modeling of these transport phenomena has to resolve two key issues: (i) the multi-length scale variations in permeability that these systems exhibit, and (ii) the inherently limited information available to quantify these property variations that necessitates posing these phenomena as stochastic processes. A stochastic variational multiscale formulation is developed to incorporate uncertain multiscale features. A stochastic analogue to a mixed multiscale finite element framework is used to formulate the physical stochastic multiscale process. Recent developments in linear and non-linear model reduction techniques are used to convert the limited information available about the permeability variation into a viable stochastic input model. An adaptive sparse grid collocation strategy is used to efficiently solve the resulting stochastic partial differential equations (SPDEs). The framework is applied to analyze flow through random heterogeneous media when only limited statistics about the permeability variation are given.

• OSTI ID: 21167747
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 2 Vol. 228; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
FINITE ELEMENT METHOD
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PERMEABILITY
POROUS MATERIALS
RADIOACTIVE WASTE DISPOSAL
RANDOMNESS
SIMULATION
STOCHASTIC PROCESSES
VARIATIONAL METHODS