Multi-scale finite-volume method for elliptic problems in subsurface flow simulation

By Patrick Jenny, Seong H. Lee, Hamdi A. Tchelepi. 2003

732 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/f39e14374db86a98c9a65323fd1f2c77ac21ceb1

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In Computational Mechanics

In Computational Theory and Mathematics

In Electrical and Electronic Engineering

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].”
Extended multiscale finite element method for mechanical analysis of heterogeneous materials (2010, methodology): “Moreover, several similar multiscale methods have been developed, such as the multiscale finite volume method [40] and the finite volume multiscale finite element method [41].”
A Multiscale Restriction-Smoothed Basis Method for Compressible Black-Oil Models (2016, methodology): “To remedy this problem, one can solve a local flow problem on each coarse block with the coarse-grid fluxes as Neumann boundary conditions to reconstruct a pressure field that in turn can be used to compute mass-conservative fluxes inside each coarse block [21, 34].”
A new multiscale computational method for elasto-plastic analysis of heterogeneous materials (2012, methodology): “Moreover, several similar multiscale methods have been developed, such as the multiscale finite volume method [ 36 ] and the finite volume multiscale finite element method [37].”
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].”
Open-source MATLAB implementation of consistent discretisations on complex grids (2012, methodology): “In the multiscale finite-volume method [ 18 , 32], the coarse-scale degrees of freedom are associated with pressure values at the vertices of the coarse grid.”
A Multiscale Mortar Mixed Finite Element Method (2007, background): “, [7, 18, 3, 1, 4, 2] and the related control volume work [33]).”
Extended multiscale finite element method for elasto-plastic analysis of 2D periodic lattice truss materials (2010, methodology): “Moreover, several similar multiscale methods have been developed, such as the multiscale finite volume method (MsFV) [31] and the multiscale finite volume element method (MsFVEM) [32].”
Multiscale mixed/mimetic methods on corner-point grids (2008, methodology): “Distinctly different, but related approaches include the paper-rev3.tex; 10/11/2006; 13:57; p.10 11 multiscale finite-volume method by Jenny, Lee and Tchelepi [21, 22], and the nested-gridding method by Gautier, Blunt and Christie [18].”
Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient (2015, unknown): “The MsFEM framework motivated a lot of interesting works and was further developed in [3, 31, 32, 35, 39].”
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.”
Multiscale finite-volume formulation for multiphase flow in porous media: black oil formulation of compressible, three-phase flow with gravity (2008, methodology): “In the original MSFV approach [ 15 ], the fine-scale velocity field is reconstructed using a second set of basis, referred to as the primal basis functions, and a block-based Schwarz overlapping technique is used to solve the hyperbolic fine-scale saturation equations (i.e., transport problem).”