scholarly journals Approximating Infinity-Dimensional Stochastic Darcy's Equations without Uniform Ellipticity

2009 ◽  
Vol 47 (5) ◽  
pp. 3624-3651 ◽  
Author(s):  
J. Galvis ◽  
M. Sarkis
Keyword(s):  
Uniform Ellipticity ◽  
Darcy’S Equations

Heat Transfer in Porous Media Heated From Above With Evaporation, Condensation, and Capillary Effects

1983 ◽  
Vol 105 (3) ◽  
pp. 485-492 ◽  
Author(s):  
K. S. Udell
Keyword(s):  
Stable State ◽  
Superheated Liquid ◽  
Phase Zone ◽  
Two Phase ◽  
Water Steam ◽  
Zone Length ◽  
Compressed Liquid ◽  
Pressure Lowering ◽  
Darcy’S Equations ◽  
Convection Dominated

Heat and mass transfer characteristics of a sand-water-steam system heated at the top and cooled at the bottom were studied. It was found that at steady-state conditions the system segregated into three regions. The top region was conduction-dominated with the voids containing a stationary superheated steam. The middle region was convection-dominated, nearly isothermal, and exhibited an upward flow of the liquid by capillary forces and a downward flow of steam due to a slight pressure gradient. The bottom portion contained a stationary compressed liquid and was also conduction dominated. The length of the two-phase convection zone was evaluated through the application of Darcy’s equations for two-phase flow and correlations of relative permeabilities and capillary pressure data. The model was in excellent agreement with the observed results, predicting a decreasing two-phase zone length with increasing heat flux. The thermodynamics of the two-phase zone were also analyzed. It was found that the vapor phase was in a superheated state as described by the Kelvin equation for vapor pressure lowering. Also, it was evident that the liquid must also be superheated for thermodynamic equilibrium to result. A stability analysis demonstrated that the superheated liquid can exist in an unconditionally stable state under conditions typical of porous systems. The degree of liquid superheat within the two-phase zone of these experiments was obtained.

scholarly journals Spectral discretization of Darcy's equations coupled with the heat equation

2015 ◽  
Vol 36 (3) ◽  
pp. 1193-1216 ◽  
Author(s):  
Christine Bernardi ◽  
Sarra Maarouf ◽  
Driss Yakoubi
Keyword(s):  
Heat Equation ◽  
Darcy’S Equations ◽  
Spectral Discretization

Darcy’s equations

2021 ◽  
pp. 379-392
Author(s):  
Alexandre Ern ◽  
Jean-Luc Guermond
Keyword(s):  
Darcy’S Equations

scholarly journals A Regularity Result for the p-Laplacian Near Uniform Ellipticity

2016 ◽  
Vol 48 (3) ◽  
pp. 2059-2075 ◽  
Author(s):  
Carlo Mercuri ◽  
Giuseppe Riey ◽  
Berardino Sciunzi
Keyword(s):  
Regularity Result ◽  
Uniform Ellipticity

Bramble--Pasciak-Type Conjugate Gradient Method for Darcy's Equations

2016 ◽  
Vol 37 (1) ◽  
pp. 469-489
Author(s):  
Faisal Fairag ◽  
Mohammed Alshahrani ◽  
Hattan Tawfiq
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Darcy’S Equations

scholarly journals Spectral discretizations of the Darcy's equations with non standard boundary conditions

2018 ◽  
Vol 10 (1) ◽  
Author(s):  
Bernard Jean-Marie
Keyword(s):  
Error Estimate ◽  
Numerical Experiments ◽  
Flow In Porous Media ◽  
Optimal Error Estimate ◽  
Discrete Solution ◽  
Optimal Error ◽  
The Third ◽  
Darcy Problem ◽  
Darcy’S Equations ◽  
Variational Formulations

This paper is devoted to the approximation of anonstandard Darcy problem, which modelizes the flow in porous media, byspectral methods: the pressure is assigned on a part of the boundary.We propose two variational formulations, as well as three spectraldiscretizations. The second discretization improves the approximation of thedivergence-free condition, but the error estimate on the pressure is notoptimal, while the third one leads to optimal error estimate with adivergence-free discrete solution, which is important for someapplications. Next, their numerical analysis is performed in detailand we present some numerical experiments which confirm the interestof the third discretization.

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