Implementation of a Locally Conservative Numerical Subgrid Upscaling Scheme for Two-Phase Darcy Flow

By Todd Arbogast. 2002

202 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1714384c5093ded4b26c6045b509a82b95779679

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In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

A comparison of multiscale methods for elliptic problems in porous media flow (2008, methodology): “The purpose of this paper is to compare and validate three selected multiscale methods in terms of accuracy, robustness, and computational complexity; a mixed multiscale finite-element method [13, 1], a two-scale conservative subgrid approach [5, 6], and a multiscale finitevolume method [25, 24].”
Domain Decomposition Preconditioners for Multiscale Flows in High Contrast Media: Reduced Dimension Coarse Spaces (2010, unknown): “It is common to use upscaled or multiscale models to solve flow and transport processes on the coarse grid [1, 3, 4, 5, 9, 21].”
Multiscale finite-volume formulation for multiphase flow in porous media: black oil formulation of compressible, three-phase flow with gravity (2008, methodology): “Arbogast [ 2 ] and Arbogast and Bryant [3] proposed a multiscale mixed finite-element method.”
Locally conservative, stabilized finite element methods for variably saturated flow (2008, background): “Variational multiscale-based approximations have since become increasingly popular [16, 37, 38] and were applied to two-phase flow in porous media in [39] as well as [40].”
Generalized multiscale finite element methods (GMsFEM) (2013, background): “, see [40, 43, 1, 3, 4, 7, 8, 20, 21, 33, 42] for upscaling and multiscale methods) attempt to approximate the solution in local (coarse-grid) regions for all input parameters without computing global snapshots of solutions.”
Deep Multiscale Model Learning (2018, background): “These approximations, e.g., typically involve a form of the coarse-grid equation [2, 23, 4, 22, 14, 7, 10, 21, 1, 20, 25, 26, 43, 41, 30, 13, 15, 11, 12], where the coarse-grid equations are formed and the parameters are computed or found via inverse problems [5, 39, 6, 42, 47].”
A Multiscale Restriction-Smoothed Basis Method for Compressible Black-Oil Models (2016, background): “Altogether, this ensures that one can easily and systematically trade accuracy for efficiency, or vice versa.”