Journal ArticleDOI
On the Closure Problem for Darcy's Law
TLDR
In this article, the Darcy's closure problem is transformed to a set of Stokes-like equations and the computational advantages of the transformed closure problem are considerable, but the computational complexity of the transformation is not discussed.Abstract:
In a previous derivation of Darcy's law, the closure problem was presented in terms of an integro-differential equation for a second-order tensor. In this paper, we show that the closure problem can be transformed to a set of Stokes-like equations and we compare solutions of these equations with experimental data. The computational advantages of the transformed closure problem are considerable.read more
Citations
More filters
Journal ArticleDOI
The Forchheimer equation : A theoretical development
TL;DR: In this article, the volume averaged momentum equation is used to derive Darcy's law with the Forchheimer correction for homogeneous porous media, and the closure problem can be used to prove that F is a linear function of the velocity, and order of magnitude analysis suggests that this linear dependence may persist for a wide range of Reynolds numbers.
Book ChapterDOI
One- and Two-Equation Models for Transient Diffusion Processes in Two-Phase Systems
Michel Quintard,Stephen Whitaker +1 more
TL;DR: In this paper, the authors examined the process of transient heat conduction for a two-phase system in terms of the method of volume averaging, and compared results from the two-equation model with results from a single-phase model.
Journal ArticleDOI
Transport in ordered and disordered porous media: volume-averaged equations, closure problems, and comparison with experiment
Michel Quintard,Stephen Whitaker +1 more
TL;DR: In this article, the authors consider transport in ordered and disordered rigid porous media and define order and disorder in terms of geometrical integrals that arise naturally in the method of volume averaging.
Journal ArticleDOI
A smoothed particle hydrodynamics model for reactive transport and mineral precipitation in porous and fractured porous media
TL;DR: In this paper, a numerical model based on smoothed particle hydrodynamics (SPH) was used to simulate reactive transport and mineral precipitation in porous and fractured porous media.
Journal ArticleDOI
Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 5. Single-Fluid-Phase Transport.
William G. Gray,Cass T. Miller +1 more
TL;DR: This work is the fifth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems and develops Classical irreversible thermodynamics formulations for species in fluids, solids, and interfaces.
References
More filters
Book
Dynamics of fluids in porous media
TL;DR: In this paper, the Milieux poreux Reference Record was created on 2004-09-07, modified on 2016-08-08 and the reference record was updated in 2016.
Journal ArticleDOI
Asymptotic Analysis of Periodic Structures
Book
Asymptotic analysis for periodic structures
TL;DR: In this article, the authors give a systematic introduction of multiple scale methods for partial differential equations, including their original use for rigorous mathematical analysis in elliptic, parabolic, and hyperbolic problems, and with the use of probabilistic methods when appropriate.
Book
Non-Homogeneous Media and Vibration Theory
TL;DR: In this article, a spectral perturbation of spectral families and applications to self-adjoint eigenvalue problems are discussed, as well as the Trotter-Kato theorem and related topics.
Book
Principles of heat transfer
TL;DR: In this paper, Kreith, Manglik, and Bohn present relevant and stimulating content in this fresh and comprehensive approach to heat transfer, acknowledging that in today's world classical mathematical solutions to Heat Transfer problems are often less influential than computational analysis.