Multicomponent fluid flow by discontinuous Galerkin and mixed methods in unfractured and fractured media

Hoteit, Hussein; Firoozabadi, Abbas

doi:10.1029/2005wr004339

Cited by 182 publications

(101 citation statements)

References 46 publications

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“…[25] For simulations of the fully resolved (fine scale) model and the local upscaling calculations (i.e., solutions of equations (7) and (8)), any discrete fracture simulation procedure [e.g., Bogdanov et al, 2003aBogdanov et al, , 2003bMonteagudo and Firoozabadi, 2004;Matthäi et al, 2005;Hoteit and Firoozabadi, 2005] could be applied. In this work we use a recently developed finite volume based discrete fracture model, presented by Karimi-Fard et al [2004] and also described (for a different application involving flow in systems characterized by thin but extensive lowpermeability compaction bands, which act as ''antifractures'') by Sternlof et al [2006].…”

Section: Governing Equations and Discrete Fracture Modelmentioning

confidence: 99%

Generation of coarse‐scale continuum flow models from detailed fracture characterizations

Karimi-Fard

Gong

Durlofsky

2006

Water Resources Research

135

101

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[1] A procedure for developing coarse-scale continuum models from detailed fracture descriptions is developed and applied. The coarse models are in the form of a generalized dual-porosity representation, in which matrix rock and fractures exchange fluid locally while large-scale flow occurs through the fracture network. The methodology developed here introduces local subgrids to resolve dynamics within the matrix and provides appropriate coarse-scale parameters describing fracture-fracture, matrix-fracture, and matrix-matrix flow. The geometry of the local subgrids, as well as the required parameters for the coarse-scale model, are determined from local flow solutions using the underlying discrete fracture model. The method is applied to two-and three-dimensional singlephase and two-phase flow problems, and the accuracy of the coarse models is assessed relative to fully resolved discrete fracture simulations. For the cases considered, it is shown that the technique is capable of generating highly accurate coarse models with many fewer unknowns than the detailed characterizations, and speedups of about a factor of 100 are achieved.

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Section: Governing Equations and Discrete Fracture Modelmentioning

confidence: 99%

Generation of coarse‐scale continuum flow models from detailed fracture characterizations

Karimi-Fard

Gong

Durlofsky

2006

Water Resources Research

135

101

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“…These techniques have been largely successful for multiphase flow problems when applied to the global flow (or pressure) equation in fractional flow formulations (Chavent et al, 1984;Gerritsen and Durlofsky, 2005;Hoteit and Firoozabadi, 2005;Chen et al, 2006). They have also been applied to Richards' equation by a number of researchers (Bergamaschi et al, 1999;Li et al, 2007a;Arrarás et al, 2009;Klausen et al, 2008;Kumar et al, 2009).…”

Section: Spatial Discretizationmentioning

confidence: 99%

Numerical Solution of Richards' Equation: A Review of Advances and Challenges

Farthing

Ogden

2017

Soil Science Soc of Amer J

261

138

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The flow of water in partially saturated porous media is of importance in fields such as hydrology, agriculture, environment and waste management. It is also one of the most complex flows in nature. The Richards' equation describes the flow of water in an unsaturated porous medium due to the actions of gravity and capillarity neglecting the flow of the non-wetting phase, usually air. Analytical solutions of Richards' equation exist only for simplified cases, so most practical situations require a numerical solution in one-two-or threedimensions, depending on the problem and complexity of the flow situation. Despite the fact that the first reasonably complete conservative numerical solution method was published in the early 1990s, the numerical solution of the Richards' equation remains computationally expensive and in certain circumstances, unreliable. A universally robust and accurate solution methodology has not yet been identified that is applicable across the range of soils, initial and boundary conditions found in practice. Existing solution codes have been modified over years to attempt to increase robustness. Despite theoretical results on the existence of solutions given sufficiently regular data and constitutive relations, our numerical methods often fail to demonstrate reliable convergence behavior in practice, especially for higher-order methods. Because of robustness, the lack of higher-order accuracy and computational expense, alternative solution approaches or methods are needed. There is also a need for better documentation of improved solution methodologies and benchmark test problems to facilitate consistent advances and avoid re-inventing of the wheel.T his review paper is intended to serve as a touchstone on the state of the science of calculating the flow of water through unsaturated porous media. As active researchers we believe it is good to occasionally take stock in what has been accomplished up to date, where things may be headed, and what important issues remain. This review concentrates on computational modeling of flow through the unsaturated zone via Richards' equation.This effort can help provide some focus to the research community and serve to help propel new research forward, particularly by those just joining the field. There are many practical problems that require calculation of one-, two-, and threedimensional fluxes in the unsaturated zone. For a much broader review of modeling soil processes, we recommend the recent paper from Vereecken et al. (2016). A detailed review of mathematical models of infiltration can be found (Assouline, 2013), while Paniconi and Putti (2015) provide historical perspective and an overview of modeling Richards' equation in the context of catchment hydrology.The equation attributed to Richards (1931) that describes the flow of water through unsaturated porous media under the action of capillarity and gravity was first published by the English mathematician and physicist Lewis Fry Richardson in 1922(Richardson, 1922. Therefore, the equation would r...

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“…Also, higher-order methods have less numerical dispersion and more accurate flow field calculations than the first-order methods. The combined mixed-hybrid finite element (MHFE) and discontinuous Galerkin (DG) methods have been used to simulate two-phase flow by (Hoteit & Firoozabadi, 2005;Mikyska & Firoozabadi, 2010). In the combined MHFE-DG methods, MHFE is used to solve the pressure equation with total velocity, and DG method is used to solve explicitly the species transport equations.…”

Section: Numerical Methods For Multi-phase Flowmentioning

confidence: 99%

Solute Transport With Chemical Reaction in Singleand Multi-Phase Flow in Porous Media

El-Amin¹,

Salama²,

Sun³

2011

Mass Transfer in Multiphase Systems and Its Applications

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Multicomponent fluid flow by discontinuous Galerkin and mixed methods in unfractured and fractured media

Cited by 182 publications

References 46 publications

Generation of coarse‐scale continuum flow models from detailed fracture characterizations

Generation of coarse‐scale continuum flow models from detailed fracture characterizations

Numerical Solution of Richards' Equation: A Review of Advances and Challenges

Solute Transport With Chemical Reaction in Singleand Multi-Phase Flow in Porous Media

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