Here u(x, t) is the fluid flux, p(x, t) the pressure, and g(x) is the gravity force, the storeage rate term c(x) is (slight) compressibility and porosity of the fluid and porous medium with sources F (x, t). The density factor has been dropped from each term of (1.1b). The flow resistance a(x) is fluid viscosity times the inverse of permeability of the porous medium. The system (1.1) is supplem...

Finite element methods for a family of systems of singular perturbation problems of a saddle point structure are discussed. The system is approximately a linear Stokes problem when the perturbation parameter is large, while it degenerates to a mixed formulation of Poisson’s equation as the perturbation parameter tends to zero. It is established, basically by numerical experiments, that most of ...

We develop new stabilized mixed finite element methods for Darcy flow. Stability and an a priori error estimate in the ‘‘stability norm’’ are established. A wide variety of convergent finite elements present themselves, unlike the classical Galerkin formulation which requires highly specialized elements. An interesting feature of the formulation is that there are no mesh-dependent parameters. N...

A new mixed, stabilized, discontinuous Galerkin formulation for Darcy flow is presented. The formulation combines several attributes not simultaneously satisfied by other methods: It is convergent for any combination of velocity and pressure interpolation higher than first-order, it exactly satisfies a mass balance on each element, and it passes twoand three-dimensional constant-flow ‘‘patch te...

We derive a numerical method for Darcy flow, hence also for Poisson’s equation in first order form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is its discretization on simplicial complexes such as triangle and tetrahedral meshes. We start by rewriting the governing equations of Darcy flow using the language of ...

Aiming at nonlinear flow in fractured porous media, based on the finite volume method, discrete equations of Darcy and Forchheimer fracture were derived, a solution method for coupling is proposed. The by proposed single intersecting verified against Frih’s solution. Based this behavior rock deep-buried tunnels under high water heads was discussed. results show that hydraulic gradient surroundi...

In this paper, the bioconvective flow in a porous square cavity containing oxytactic microorganism in the presence of chemical reaction is investigated. The bioconvection flow and heat transfer in porous media are formulated based on the Darcy model of Boussinesq approximation. The governing partial differential equations are solved using the Galerkin finite element method. The computational nu...