The Flow through saturated-unsaturated porous media is extremely important in various natural and industrial based applications. While the Darcy's law with various modifications are used to model the flow through a porous media, the flow through unsaturated porous media is largely based on conservation of mass and modified Darcy's law where non-linear relationship exists between the p...

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...

This paper presents studies on applying the novel weak Galerkin finite element method (WGFEM) to a two-phase model for subsurface flow, which couples the Darcy equation for pressure and a transport equation for saturation in a nonlinear manner. The coupled problem is solved in the framework of operator decomposition. Specifically, the Darcy equation is solved by theWGFEM, whereas the saturation...

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...

In this paper, we studied the effects of heat transfer and magnetic field on the peristaltic flow of a Jeffrey fluid through a porous medium in an asymmetric channel under the assumptions of long wavelength and low Reynolds number. Expressions for the velocity and pressure gradient are obtained analytically. The effects of Hartmann number, Darcy number, phase shift, Jeffrey fluid parameter and ...

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...

An implementation of a coupled Navier-Stokes/Darcy model based on different Dune discretization modules is presented. The Darcy model is taken from DuMux, the Navier-Stokes model is implemented on top of Dune-PDELab, and the coupling is done with help of Dune-MultiDomain together with some project-specific auxiliary code. The Navier-Stokes model features one fluid phase, the Darcy model two flu...

Stress waves contain useful information about the properties of porous materials; they can be recovered through different non-destructive testing methods such as crosswell, vertical seismic profile, borehole logging as well as sonic tests. In all these methods, it is crucial to assess the effects of frequency on wave attributes including velocity and intrinsic attenuation. The dependency of per...

The present analysis investigates non-Darcy forced convective heat transfer in a channel confined by two parallel walls subjected to uniform heat flux in a highly porous medium saturated with a non-Newtonian power-law fluid. Extensive numerical integrations have been carried out utilizing the Brinkman-Forchheimer extension of the Darcy model in order to study the effects of pseudoplasticity, an...