Topological groundwater hydrodynamics is an emerging subdiscipline in the mechanics of ¯uids in porous media whose objective is to investigate the invariant geometric properties of subsurface ¯ow and transport processes. In this paper, the topological characteristics of groundwater ¯ows governed by the Darcy law are studied. It is demonstrated that: (i) the topological constraint of zero helici...

This investigation deals with the numerical simulation of entropy generation at mixed convection flow in a lid-driven saturated porous cavity submitted to a magnetic field. The magnetic field is applied in the direction that is normal to the cavity cross section. The governing equations, written in the Darcy–Brinkman–Forchheimer formulation, are solved using a numerical code based on the Contro...

The most effective simulations of the multi-physics coupling of groundwater to surface water must involve employing the best groundwater codes and the best surface water codes. Partitioned methods, which solve the coupled problem by successively solving the sub-physics problems, have recently been studied for the Stokes-Darcy coupling with convergence established over bounded time intervals (wi...

We present an overview of a modern, efficient approach for uncoupling groundwater–surface water flows governed by the fully evolutionary Stokes–Darcy equations. Referred to as non-iterative partitioned methods, these algorithms treat the coupling terms explicitly and at each time level require only one Stokes and one Darcy sub-physics solve, thus taking advantage of existing solvers optimized f...

Darcy’s law has long been used to describe the flow in porous media. Despite progress that took place oil production industry research, it became clear there is a loss of pressure, especially area near wellbore region, where not applicable. For this reason, Forchheimer presented his equation 1910, he added new term dealing with pressure due inertial forces by introducing term, β coefficient, in...

This paper presents a new stabilized finite element method for the Darcy–Stokes equations also known as the Brinkman model of lubrication theory. These equations also govern the flow of incompressible viscous fluids through permeable media. The proposed method arises from a decomposition of the velocity field into coarse/resolved scales and fine/unresolved scales. Modelling of the unresolved sc...

The gas transport in shale nanopores is always one of the major concerns in terms of the development of shale gas reservoirs. In this study, the gas flow regimes in shale nanopores were classified and analyzed according to Knudsen number. Then the gas flow model considering Darcy flow, slip flow, transition flow, molecular free flow and adsorption effect was proposed to evaluate the gas flow be...

A general form of the double porosity model of single phase flow in a naturally fractured reservoir is derived from homogenization theory. The microscopic model consists of the usual equations describing Darcy flow in a reservoir, except that the porosity and permeability coefficients are highly discontinuous. Over the matrix domain, the coefficients are scaled by a parameter representing the s...

The heat transfer rate from an isothermal vertical plate placed next to saturated high permeability porous media is studied experimentally and analytically. The media used arc polyurethane foams saturated with air. An integral method is applied in predicting the heat transfer rate by including the non-Darcy effects, which are expected to be significant for high permeabilities and high Rayleigh ...