Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under fi...

In the present paper behavior of free convective boundary layer flow an electrically con-ducting visco-elastic,incompressible fluid through a porous medium over continuously moving surface in presence uniform magnetic field with constant suction is studied. A assumed to be applied perpendicularly surface. similarity transformation used which reduces partial differential equation ordinary equati...

Abstract. It is shown that there exists a weak solution to a degenerate and singular elliptic-parabolic partial integro-differential system of equations. These equations model two-phase incompressible flow of immiscible fluids in either an ordinary porous medium or in a naturally fractured porous medium. The full model is of dual-porosity type, though the single porosity case is covered by sett...

We carry out the effect of the pulsatile flow on peristaltic motion of an incompressible conducting micropolar fluid through porous medium in a channel bounded by flexible walls.Problem formulation in a wave frame of reference is presented. An oscillatory time dependent flux is being imposed on the peristaltic flow. The non-linear equations governing the flow through porous medium under the eff...

We study the incompressible limit of porous medium equation with a right hand side representing either source or sink term, and an injection boundary condition. This model can be seen as simplified description non-monotone motions in tumor growth crowd motion, generalizing congestion-only studied recent literature (\cite{AKY}, \cite{PQV}, \cite{KP}, \cite{MPQ}). characterize density, which solv...

We consider materials with large pores interconnected by thin long channels saturated with an incompressible fluid. In the absence of fluid flow, solute transport in the porous network is diffusion controlled, however, solute transport can be enhanced when the porous network is subjected to a cyclic flow with zero time average velocity. We develop a mathematical model to analyze this physical p...

Modeling the interaction between surface and subsurface flow is a challenging environmental problem. One such example is the simulation of transport of contaminants through rivers into the aquifers. Mathematically, this complex problem can be modeled by the coupled system of Stokes and Darcy equations. The aim of this paper is to formulate and analyze a discontinuous finite element method for t...

A novel numerical formulation of the two-phase macroscopic balance equations governing the flow field in incompressible porous media is presented. The numerical model makes use of the Weighted Average Flux (WAF) method and Total Variation Diminishing (TVD) flux limiting techniques, and results in a second-order accurate scheme. A shock tube study was carried out to examine the interaction of a ...

This research paper presents an incompressible smoothed particle hydrodynamics (ISPH) technique to investigate a regular wave overtopping on the coastal structure of different types. The SPH method is a mesh-free particle modeling approach that can efficiently treat the large deformation of free surface. The incompressible SPH approach employs a true hydrodynamic formulation to solve the fluid ...

The steady flow of an electrically conducting, incompressible micropolar fluid in a narrow gap between two concentric rotating vertical cylinders, with porous lining on inside of outer cylinder, under an imposed axial magnetic field is studied. Beavers and Joseph slip condition is taken at the porous lining boundary. The velocity profiles, coefficient of skin friction on the cylinders are calcu...