We develop a finite element discretization and multigrid solver for a Darcy-Stokes system of three dimensional vuggy porous media, i.e., porous media with cavities. The finite element method uses low order mixed finite elements in the Darcy and Stokes domains, and special transition elements near the Darcy-Stokes interface to allow for tangential discontinuities implied by the Beavers-Joseph bo...

We propose and analyze a hybrid discontinuous Galerkin method for the solution of incompressible flow problems, which allows to deal with pure Stokes, pure Darcy, and coupled Darcy-Stokes flow in a unified manner. The flexibility of the method is demonstrated in numerical examples.

Phonological rules introduce variation in word forms that listeners have to compensate for. We previously showed (Darcy 2002; Darcy et al., to appear) that compensation for phonological variation in perception is driven by languagespecific mechanisms. In particular, English speakers compensate more for place assimilation than for voicing assimilation, whereas the reverse holds for French speake...

The diffusion driven by the gradient of chemical potential (by Fick/Darcy law) in deforming continua at large strains is formulated reference configuration with both law and capillarity (i.e. concentration gradient) term considered actual configurations time. Static situations are analysed direct method. Evolution (dynamical) problems treated Faedo-Galerkin method, ...

The Forchheimer equation is widely used in studying non-Darcy flow. Non-Darcy flow coefficient β the generally thought to be positive, and there are few studies on negative values. In this work, we performed seepage tests sandstone samples with single, T-shaped, Y-shaped fractures under different confining pressures, water angles analyze nonlinear behaviors features of Forchheimer’s coefficient...

The hallmark of malignant tumours is their spread into neighbouring tissue and metastasis to distant organs, which can lead to life threatening consequences. One of the defining characteristics of aggressive tumours is an unstable morphology, including the formation of invasive fingers and protrusions observed both in vitro and in vivo. In spite of extensive biological, clinical and modelling s...

This paper is devoted to the homogenizat ion of the Stokes or Navier-Stokes equations with a Dirichlet boundary condit ion in a domain containing many tiny solid obstacles, periodically distributed in each direction of the axes. For obstacles of critical size it was established in Part I that the limit problem is described by a law of Brinkman type. Here we prove that for smaller obstacles, the...

We measure the pressure difference during two-phase flow across a sandstone sample for range of injection rates and fractional flows water, wetting phase, an imbibition experiment. quantify onset transition from linear relationship between rate gradient to nonlinear power-law dependence. show that (Darcy) exponent in is function flow. use energy balance accurately predict intermittency flows, f...

It is conjectured that Darcy’s law governs the motion of compressible porous media flow in large time. This has been justified for one-dimensional isentropic flows. In this work, we show the conjecture is true for one-dimensional adiabatic flows with generic small smooth initial data. © 2004 Elsevier Inc. All rights reserved.

In this chapter a general model for the two-phase fluid flow in porous media is presented, together with its simplified form, known as the Richards equation, which is applicable (under specific assumptions) to describe water flow in the vadose zone. In each case the governing equations are formulated at the Darcy scale, using the capillary pressure–saturation relationship and an empirical exten...