A solid tumor is investigated as porous media for fluid flow simulation. Most of the studies use Darcy model for porous media. In Darcy model, the fluid friction is neglected and a few simplified assumptions are implemented. In this study, the effect of these assumptions is studied by considering Brinkman model. A multiscale mathematical method which calculates fluid flow to a solid tumor is us...

We numerically investigate the pulsatile flow and heat transfer of a micropolar fluid through a Darcy-Forchhmeir porous channel in the presence of wall transpiration. We use the central difference approximations for the spatial derivatives, whereas the time integration has been performed by employing the three steps explicit Runge-Kutta method to obtain the numerical solution. It i...

In this paper, we consider 2D and 3D Darcy-Stokes interface problems. These equations are related to Brinkman model that treats both Darcy’s law and Stokes equations in a single form of PDE but with strongly discontinuous viscosity coefficient and zerothorder term coefficient. We present three different methods to construct uniformly stable finite element approximations. The first two methods a...

In this paper lattice-Boltzmann equation method is used to simulate non-Darcy flow in porous media. 2-D in-line and staggered arrangements of uniform cylinders have been considered. The results of a comprehensive computational evaluation are reported: the range of validity of Darcy-Forchheimer equation is investigated and correlations for macroscopic transport properties are presented (i. e., f...

In this article, we analyze the flow of a fluid through a coupled Stokes-Darcy domain. The fluid in each domain is non-Newtonian, modeled by the generalized nonlinear Stokes equation in the free flow region and the generalized nonlinear Darcy equation in the porous medium. A flow rate is specified along the inflow portion of the free flow boundary. We show existence and uniqueness of a variatio...

rockfill dams are accounted as useful measures in watershed management projects. how-ever, the sediment transport through the rockfill materials, could impact their lifetime duration. previously, researches have been conducted to describe the various hydraulically issues of the flow passing through these structures however; there is no general relationship to estimate the sediment transport rat...

This paper concerns the discretization of multiphase Darcy flows, in the case of heterogeneous anisotropic porous media and general 3D meshes used in practice to represent reservoir and basin geometries. An unconditionally coercive and symmetric vertex centred approach is introduced in this paper. This scheme extends the Vertex Approximate Gradient scheme (VAG), already introduced for single ph...

The relation formulated by Swamee and Jain through the combination of the Darcy-Weisbach, on the one hand, and the Colebrook-White equation, on the other, in order to eliminate the Darcy-Weisbach resistance coefficient f, was placed in dimensionless form in two different ways. Each of the new equations contains three dimensionless variables and thus it can be depicted on a single diagram as a f...

Analysis of non-laminar flows in coarse alluvial beds has a wide range of applications in various civil engineering, oil and gas, and geology problems. Darcy equation is not valid to analyze transient and turbulent flows, so non-linear equations should be applied. Non-linear equations are classified into power and binomial equations. Binomial equation is more accurate in a wide range of velocit...

Darcy flow is a steady-state model for laminar flow of a fluid through a porous medium. The present work proposes an extended model of laminar Darcy flow by introducing dynamic pressure and velocity to the classical formulation. The solution of the proposed time-space model is attained by discretizing the problem with a stabilized mixed Galerkin method in space and a forward Euler method in tim...