Keywords: Modeling. Flow in porous media. Flow in aquifers. Transport in porous media. Saturated flow. Darcy's law. Dispersion. Variable density flow and transport.

Colloids may have an important role in regulating the structure and function of groundwater ecosystems, and may influence the migration of low solubility contaminants in groundwater. There is, however, a degree of uncertainty about how colloids behave under the variable hydrogeochemical and hydrodynamic conditions that occur during managed aquifer recharge. We used an online monitoring system t...

The system of unsteady Darcy’s equations considered here models the time-dependent flow of an incompressible fluid such as water in a rigid porous medium. We propose a discretization of this problem that relies on a backward Euler’s scheme for the time variable and finite elements for the space variables. We prove a priori error estimates that justify the optimal convergence properties of the d...

Fractional advection–dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by uid ow in a porous medium. In this paper we develop practical numerical methods to solve one dimensional fractional advection–dispersion equations with variable coe1cients on a 2nite domain. The practical application of these results is illustrated by modeling a radia...

In this paper, we examine the combined effects of thermal radiation, buoyancy force and magnetic field on oscillatory flow of a conducting optically thin dusty fluid through a vertical channel filled with a saturated porous medium. The governing partial differential equations are obtained and solved analytically by variable separable method. Numerical results depicting the effects of various em...

We consider three-dimensional convection of an incompressible fluid saturated in a parallelepiped with a porous medium. A mimetic finite-difference scheme for the Darcy convection problem in the primitive variables is developed. It consists of staggered nonuniform grids with five types of nodes, differencing and averaging operators on a two-nodes stencil. The nonlinear terms are approximated us...

A recent paper reported capillary rise and evaporation experiments in metallic wicks, as well as a mathematical model. The authors found a consistent discrepancy between the model predictions and data: The model over-predicted the capillary height rise by about 20%. The model used assumes that the porous medium is either fully wet or dry, an assumption that is particularly unsuited to evaporati...

Porous media has interesting features in compared with free flame combustion due to the extended of the lean flammability limits and lower emissions. Advanced new generation of internal combustion (IC) engines are expected to have far better emissions levels both gaseous and particulate matter, at the same time having far lower fuel consumption on a wide range of operating condition. These c...

The study of differential equations and variational problems with variable exponent has been a new and interesting topic. Its interest is widely justified with many physical examples, such as nonlinear elasticity theory, electrorheological fluids, etc. (see [1, 2]). It also has wide applications in different research fields, such as image processing model (see e.g. [3,4]), stationary thermorheo...

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