An efficient, high-order perturbation approach for flow in random porous media via Karhunen-Loève and polynomial expansions

By Dongxiao Zhang, Zhiming Lu. 2004

374 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Environmental Engineering, Geochemistry and Petrology

View Paper: https://www.semanticscholar.org/paper/eef1a3eea2b7fdbda804b95d646c4011a6971982

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In Civil and Structural Engineering

In Environmental Engineering

In Geochemistry and Petrology

Citations in the corpus

Data assimilation for transient flow in geologic formations via ensemble Kalman filter (2006, methodology): “The initial realizations of log hydraulic conductivity field for the EnKF system are generated by Karhunen– Loeve expansion [29] with given statistics.”
A Polynomial Chaos-Based Kalman Filter Approach for Parameter Estimation of Mechanical Systems (2010, methodology): “Zhang and Lu [38] combined the Karhunen–Loeve decomposition and perturbation methods with polynomial expansions in order to evaluate higher-order moments for saturated flow in randomly heterogeneous porous media.”
Wiener's Polynomial Chaos for the Analysis and Control of Nonlinear Dynamical Systems with Probabilistic Uncertainties [Historical Perspectives] (2013, background): “Since a research monograph [15] implemented PCEs in terms of Hermite polynomials for linear elastic problems, PCEs have become broadly used in a wide variety of fields including in stochastic differential equations [19], [21], fluid dynamics [22]–[25], aircraft operations [26], environmental applica”
Deep Learning of Subsurface Flow via Theory-guided Neural Network (2019, background): “…variance and the correlation length of the random field, respectively, the eigenvalues and eigenfunctions can be solved analytically or semi-analytically, as given below (Zhang & Lu, 2004): The eigenvalues and eigenfunctions are then combined in each direction, which can be expressed as follows:”
Stochastic collocation and mixed finite elements for flow in porous media (2008, methodology): “7) was used to generate the KL expansion of an isotropic permeability field, as given in [44].”
Impact of sampling volume on the probability density function of steady state concentration (2008, methodology): “, 1978] and in nonstationary fields [Li and McLaughlin, 1991, 1995], by higher-order approximations [Neuman and Orr, 1993; Zhang and Lu, 2004] and numerical simulations [Zhang, 1998; Lu and Zhang, 2004].”
Efficient geostatistical inverse methods for structured and unstructured grids (2006, methodology): “The KL expansion has been used in uncertainty propagation in conjunction with both Winer polynomial chaos expansions [e.g., Ghanem and Spanos, 1991; Xiu and Karniadkis, 2002] and small-perturbation expansions [e.g., Zhang and Lu, 2004].”
Probabilistic collocation method for flow in porous media: Comparisons with other stochastic methods (2007, methodology): “In the KLME, the number of terms included in approximating h(i)(x) can be distinctly selected for each order i [Zhang and Lu, 2004].”
Deep Convolutional Encoder‐Decoder Networks for Uncertainty Quantification of Dynamic Multiphase Flow in Heterogeneous Media (2018, methodology): “Note that if this random field is parameterized using the Karhunen-Loève expansion [Zhang and Lu, 2004], ≈ 800 expansion terms will be needed to preserve ≈ 95% of the field variance.”