Journal ArticleDOI
Numerical simulation of three-dimensional saturated flow in randomly heterogeneous porous media
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This paper presents a numerical method for simulating flow fields in a stochastic porous medium that satisfies locally the Darcy equation, and has each of its hydraulic parameters represented as one realization of a three-dimensional random field using the Turning Bands method.Abstract:
This paper presents a numerical method for simulating flow fields in a stochastic porous medium that satisfies locally the Darcy equation, and has each of its hydraulic parameters represented as one realization of a three-dimensional random field. These are generated by using the Turning Bands method. Our ultimate objective is to obtain statistically meaningful solutions in order to check and extend a series of approximate analytical results previously obtained by a spectral perturbation method (L. W. Gelhar and co-workers). We investigate the computational aspects of the problem in relation with stochastic concepts. The difficulty of the numerical problem arises from the random nature of the hydraulic conductivities, which implies that a very large discretized algebraic system must be solved. Indeed, a preliminary evaluation with the aid of scale analysis suggests that, in order to solve meaningful flow problems, the total number of nodes must be of the order of 106. This is due to the requirement that Δxi ≪ gli ≪ Li, where Δxi is the mesh size, λi is a typical correlation scale of the inputs, and Li is the size of the flow domain (i = 1, 2, 3). The optimum strategy for the solution of such a problem is discussed in relation with supercomputer capabilities. Briefly, the proposed discretization method is the seven-point finite differences scheme, and the proposed solution method is iterative, based on prior approximate factorization of the large coefficient matrix. Preliminary results obtained with grids on the order of one hundred thousand nodes are discussed for the case of steady saturated flow with highly variable, random conductivities.read more
Citations
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Journal ArticleDOI
A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media
Thomas Y. Hou,Xiao-Hui Wu +1 more
TL;DR: This paper studies a multiscale finite element method for solving a class of elliptic problems arising from composite materials and flows in porous media, which contain many spatial scales and proposes an oversampling technique to remove the resonance effect.
Journal ArticleDOI
Calculating equivalent permeability: a review
Philippe Renard,G. de Marsily +1 more
TL;DR: This article shows how equivalence is defined by using a criterion of flow or of the energy dissipated by viscous forces and explains the two different concepts of effective permeability and block permeability.
Journal ArticleDOI
Universal scaling of hydraulic conductivities and dispersivities in geologic media
TL;DR: In this article, a self-similar hierarchy of log hydraulic conductivity fields with mutually uncorrelated increments is proposed, each field having its own exponential autocovariance, associated integral scale, and variance that increases as a power of scale.
Journal ArticleDOI
A Reassessment of the Groundwater Inverse Problem
TL;DR: In this paper, the authors present a functional formulation of the groundwater flow inverse problem that is sufficiently general to accommodate most commonly used inverse algorithms, including the Gaussian maximum a posteriori (GAP) algorithm.
Journal ArticleDOI
Numerical simulation of solute transport in three-dimensional, randomly heterogeneous porous media
TL;DR: In this paper, a three-dimensional solute transport model is developed to study detailed contaminant movements through large heterogeneous flow systems in porous media, based upon a random walk particle method.
References
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Journal ArticleDOI
Iterative solution of implicit approximations of multidimensional partial differential equations
TL;DR: In this article, a new iterative method has been developed for solving the large sets of algebraic equations that arise in the approximate solution of multidimensional partial differential equations by implicit numerical techniques.
Journal ArticleDOI
An iterative solution method for linear systems of which the coefficient matrix is a symmetric -matrix
TL;DR: A particular class of regular splittings of not necessarily symmetric M-matrices is proposed, if the matrix is symmetric, this splitting is combined with the conjugate-gradient method to provide a fast iterative solution algorithm.
Journal ArticleDOI
Three‐dimensional stochastic analysis of macrodispersion in aquifers
Lynn W. Gelhar,Carl L. Axness +1 more
TL;DR: In this article, the dispersive mixing resulting from complex flow in three-dimensionalally heterogeneous porous media is analyzed using stochastic continuum theory, which is consistent with controlled field experiments and Monte Carlo simulations.
Journal ArticleDOI
The intrinsic random functions and their applications
TL;DR: The intrinsic random functions (IRF) are a particular case of the Guelfand generalized processes with stationary increments and constitute a much wider class than the stationary RF, and are used in practical applications for representing nonstationary phenomena as discussed by the authors.
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