We consider a model for flow in a porous medium with a fracture in which the flow in the fracture is governed by the Darcy-Forchheimer law while that in the surrounding matrix is governed by Darcy’s law. We give an appropriate mixed, variational formulation and show existence and uniqueness of the solution. To show existence we give an analogous formulation for the model in which the Darcy-Forc...

Incompressible, axisymmetric laminar flow downstream of a porous expansion is simulated. Effect of the Darcy number and inertia coefficient on flow and heat transfer characteristics downstream of the expansion is investigated. The simulation revealed circulation downstream of the expansion. Decreasing the Darcy number is shown to decrease the circulation region. The Nusselt number, friction coe...

A mathematical and numerical model describing chemical transport in a Stokes– Darcy flow system is discussed. The flow equations are solved through domain decomposition using classical finite element methods in the Stokes region and mixed finite element methods in the Darcy region. The local discontinuous Galerkin (LDG) method is used to solve the transport equation. Models dealing with couplin...

The flow past an impermeable sphere embedded in a fluid saturated porous medium was studied numerically considering valid the Brinkman−Forchheimer−Darcy (or Brinkman−Hazen−Dupuit−Darcy) model. The flow is viscous, laminar, axisymmetric, steady and incompressible. The porous medium is isotropic, rigid and homogeneous. The stream function vorticity equations were solved numerically in spherical c...

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...

abstract rockfill dams are usually used for affecting the flood and reducing the peak discharge. the materials used in these dams will usually make the flow turbulent, therefore darcy's law can not be used for this kind of dams and the equations based on the non-darcy flow must be applied. non-darcy flow equations are showed in two general ways including: and .one of the main parameters for flo...

The Workshop was asked by Pall Corporation to consider ways in which membrane morphology may be characterized, and how such characterization can be used to assess filtration efficiency. The working group considered a variety of different (but related) approaches, which are outlined below but which will be described in more detail in the forthcoming report. 1 Darcy flow model In an effort to cha...

Please cite this article in press as: M. Sankar et a Mass Transfer (2012), http://dx.doi.org/10.1016 Double-diffusive convection in a vertical annulus filled with a fluid-saturated porous medium is numerically investigated with the aim to understand the effects of a discrete source of heat and solute on the fluid flow and heat and mass transfer rates. The porous annulus is subject to heat and m...

There has been a surge of work on models for coupling surface-water with groundwater flows which is at its core the Stokes-Darcy problem. The resulting (Stokes-Darcy) fluid velocity is important because the flow transports contaminants. The analysis of models including the transport of contaminants has, however, focused on a quasi-static Stokes-Darcy model. Herein we consider the fully evolutio...

The goal of this short course is to review the analysis and the systematic discretization of saddlepoint systems that arise in the weak formulation of certain fluid flow problems by Galekrin methods. To demonstrate the applicability of the main arguments in various situations, we consider the slow flow of water through a channel surrounded by a porous aquiver. While the free flow of the fluid m...