In this paper we consider a modification to Darcy equation by taking into account the dependence of viscosity on the pressure. We present a stabilized mixed formulation for the resulting governing equations. Equal-order interpolation for the velocity and pressure is considered, and shown to be stable (which is not the case under the classical mixed formulation). The proposed mixed formulation i...

The unsteady two-dimensional laminar g-Jitter mixed convective boundary layer flow of Cu-water and Al2O3-water nanofluids past a permeable stretching sheet in a Darcian porous is studied by using an implicit finite difference numerical method with quasi-linearization technique. It is assumed that the plate is subjected to velocity and thermal slip boundary conditions. We have considered tempera...

In this work we present control volume multiscale methods which address problems on the interaction between pore scale and Darcy scale. For the case when linear equations govern the flow on the pore scale our solution converges to semi-analytical solution. Moreover, the method also extends to non-linear problems governed by NavierStokes equations. We show numerical results illustrating the appl...

The free conv ection boundary layer flow of a Darcy-Brinkman fluid that is induced by a constant-temperature horizontal semi-infinite surface embedded in a fluid-saturated porous medium is inv estigated in this work. It is shown that both the Darcy and Rayleigh numbers may be scaled out of the boundary layer equations, leav ing a parabolic system of equations with no parameters to vary. The equ...

New mimetic discretizations of diffusion-type equations (for instance, equations modeling single phase Darcy flow in porous media) on unstructured polygonal meshes are derived. The first order convergence rate for the fluid velocity and the second-order convergence rate for the pressure on polygonal, locally refined and non-matching meshes are demonstrated with numerical experiments.

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...

We study the existence of weak solutions to a Cahn–Hilliard–Darcy system coupled with a convection-reaction-diffusion equation through the fluxes, through the source terms and in Darcy’s law. The system of equations arises from a mixture model for tumour growth accounting for transport mechanisms such as chemotaxis and active transport. We prove, via a Galerkin approximation, the existence of g...

Hybrid or multiphysics algorithms provide an efficient computational tool for combining microand macroscale descriptions of physical phenomena. Their use becomes imperative when microscale descriptions are too computationally expensive to be conducted in the whole domain, while macroscale descriptions fail in a small portion of the computation domain. We present a hybrid algorithm to model a ge...

Hall effects on an unsteady MHD flow of a viscous incompressible electrically conducting fluid between two rotating disks with non-coincident parallel axes embedded in a porous medium have been studied. The governing equations have been solved analytically using the Laplace transform technique. The effects of rotation parameter, Hall parameter, Hartmann number and Darcy number have been conside...

Abstract—This work deals with the problem of MHD mixed convection in a completely porous and differentially heated vertical channel. The model of Darcy-Brinkman-Forchheimer with the Boussinesq approximation is adopted and the governing equations are solved by the finite volume method. The effects of magnetic field and buoyancy force intensities are given by the Hartmann and Richardson numbers r...