Journal ArticleDOI
An efficient, high-order perturbation approach for flow in random porous media via Karhunen-Loève and polynomial expansions
Dongxiao Zhang,Zhiming Lu +1 more
Reads0
Chats0
TLDR
In this article, a higher-order solution of the means and variance of hydraulic head for saturated flow in randomly heterogeneous porous media was obtained by the combination of Karhunen-Loeve decomposition, polynomial expansion, and perturbation methods.About:
This article is published in Journal of Computational Physics.The article was published on 2004-03-01. It has received 342 citations till now. The article focuses on the topics: Polynomial expansion & Covariance function.read more
Citations
More filters
Journal ArticleDOI
Data assimilation for transient flow in geologic formations via ensemble Kalman filter
Yan Chen,Dongxiao Zhang +1 more
TL;DR: In this study, the ensemble Kalman filter (EnKF) approach is used for continuously updating model parameters such as hydraulic conductivity and model variables such as pressure head while simultaneously providing an estimate of the uncertainty through assimilating dynamic and static measurements, without resorting to the explicit computation of the covariance or the Jacobian of the state variables.
Journal ArticleDOI
Probabilistic collocation method for flow in porous media: Comparisons with other stochastic methods
TL;DR: In this article, an efficient method for uncertainty analysis of flow in random porous media is explored, on the basis of combination of Karhunen-Loeve expansion and probabilistic collocation method (PCM).
Journal ArticleDOI
Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics
TL;DR: A numerical method based on Wiener Chaos expansion is proposed and applied to solve the stochastic Burgers and Navier-Stokes equations driven by Brownian motion and it is demonstrated that for short time solutions the numerical methods are more efficient and accurate than those based on the Monte Carlo simulations.
Journal ArticleDOI
An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations
Xiang Ma,Nicholas Zabaras +1 more
TL;DR: The proposed method provides accurate results for stochastic dimensionality as high as 500 even with large-input variability and the efficiency of the proposed method is examined by comparing with Monte Carlo (MC) simulation.
Journal ArticleDOI
Deep Convolutional Encoder-Decoder Networks for Uncertainty Quantification of Dynamic Multiphase Flow in Heterogeneous Media
TL;DR: In this paper, a deep convolutional encoder-decoder neural network was proposed to characterize the high-dimensional time-dependent outputs of the dynamic multi-phase flow model with a 2500-dimensional stochastic permeability field.
References
More filters
Book
Methods of Mathematical Physics
Richard Courant,David Hilbert +1 more
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Book
Probability theory
TL;DR: These notes cover the basic definitions of discrete probability theory, and then present some results including Bayes' rule, inclusion-exclusion formula, Chebyshev's inequality, and the weak law of large numbers.
Book
Stochastic Finite Elements: A Spectral Approach
Roger Ghanem,Pol D. Spanos +1 more
TL;DR: In this article, a representation of stochastic processes and response statistics are represented by finite element method and response representation, respectively, and numerical examples are provided for each of them.
Book
Flow and Transport in Porous Formations
TL;DR: In this article, the authors presented a systematic and comprehensive approach to analyze the large scale heterogeneity of aquifers and its effect on the transport of contaminant in subsurface hydrology.
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.