Homogenization of a Darcy–Stokes system modeling vuggy porous media

By Todd Arbogast, H. Lehr. 2006

214 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/c8272c79c2c6701839e2dc5a640a557c5a383eee

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In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Time-dependent coupling of Navier–Stokes and Darcy flows (2013, methodology): “For instance, the reader can refer to the works of Arbogast and Lehr in [3], of Arbogast and Brunson in [2], of Burman and Hansbo in [7], of Cao et al.”
Numerical Calculation of Equivalent Permeability Tensor for Fractured Vuggy Porous Media Based on Homogenization Theory (2011, methodology): “[3, 7, 8] modeled the vuggy porous medium on the fine scale using Stokes equations in the vugs, Darcy’s law in the porous rock, and the BeaversJoseph-Saffman boundary condition on the interface between the two regions.”
NON-MATCHING MORTAR DISCRETIZATION ANALYSIS FOR THE COUPLING STOKES-DARCY EQUATIONS (2007, background): “There are previous works addressing such issues [8, 13, 20, 26] as well as related problems such as Stokes-Laplacian systems [10, 11, 25], Stokes-Navier Stokes [16, 24], and preconditioned iterative methods [10, 12, 13, 14], among others [2, 21].”
Analysis of finite element methods for the Brinkman problem (2010, unknown): “[11, 1, 2, 3, 15].”
A discretization and multigrid solver for a Darcy–Stokes system of three dimensional vuggy porous media (2009, methodology): “The macromodel derived in [4] is obtained from the micromodel, appropriately scaled, using homogenization theory under certain mathematical assumptions.”
H(div)-conforming Finite Elements for the Brinkman Problem (2011, background): “For a derivation of and details on the equations we refer to [17, 1, 2, 3, 21].”
A computational method for approximating a Darcy–Stokes system governing a vuggy porous medium (2007, background): “We use the analytical solution of [2].”
A Comparison of Various Methods for the Numerical Evaluation of Porous Media Permeability Tensors from Pore-Scale Geometry (2016, background): “This is indeed the case, as has been demonstrated in [5, 27, 16, 15].”