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...

This paper presents the study of convective heat and mass transfer characteristics of an incompressible MHD viscoelastic fluid past an infinite vertical plate immersed in a porous medium with chemical reaction and ion slip effects. Highly nondimensional governing equations are solved analytically by perturbation scheme. The analytical expressions for velocity, shearing stress, temperature, conc...

We show that the widely used model governing the motion of two incompressible immiscible fluids in a possibly heterogeneous porous medium has a formal gradient flow structure. More precisely, the fluid composition is governed by the gradient flow of some non-smooth energy. Starting from this energy together with a dissipation potential, we recover the celebrated DarcyMuskat law and the capillar...

We study numerically a new model describing the multiscale flow of a single-phase incompressible fluid and transport of a dissolved chemical by advection and diffusion through a heterogeneous porous medium without the usual assumptions of scale separation. The new model includes as special cases the classical homogenized model as well as the double porosity models, but it is characterized by th...

We study numerically a new model describing the multiscale flow of a singlephase incompressible fluid and transport of a dissolved chemical by advection and diffusion through a heterogeneous porous medium without the usual assumptions of scale separation. The new model includes as special cases the classical homogenized model as well as the double porosity models, but it is characterized by the...

Abstract: In this paper, we consider the unsteady hydromagnetic incompressible viscous fluid flow through a porous medium in a horizontal channel under prescribed discharge, under the influence of inclined magnetic field. The undisturbed flow is due to a constant pressure gradient and the unsteadiness in the flow is created by imposing a time – dependent flux condition. The solutions for the ve...

We consider the problem of the evolution of the interface given by two incompressible fluids through a porous medium, which is known as the Muskat problem and in two dimensions it is mathematically analogous to the two-phase Hele-Shaw cell. We focus on a fluid interface given by a jump of densities, being the equation of the evolution obtained using Darcy’s law. We prove local well-posedness wh...

This paper deals with the study of ureteral peristalsis in cylindrical tube through porous medium. In reality, there are solid particles present in the flow, but it is necessary to understand the behaviour of the fluid flow. The flow is analyzed for a single traveling wave in an axisymmetric tube with an incompressible, Newtonian fluid. The wavelength of the traveling wave assumed to be large. ...

We study Soret-Dufour and radiation effects on unsteady viscous incompressible MHD flow along semi infinite inclined permeable moving plate with variable temperature and mass diffusion embedded in a porous medium numerically, by taking into account the effect of viscous dissipation. The dimensionless governing equations of flow field are solved numerically by Crank-Nicolson finite difference me...

A model for two-phase, incompressible, immiscible fluid flow in a highly fractured porous medium is derived as a simplification of a much more detailed dual-porosity model. This simplified model has a nonlinear matrixfracture interaction, and it is more general than similar existing “transfer function” models. It is computationally less complex than the detailed model, and simulation results ar...