abstract rockfill dams are usually used for affecting the flood and reducing the peak discharge. the materials used in these dams will usually make the flow turbulent, therefore darcy's law can not be used for this kind of dams and the equations based on the non-darcy flow must be applied. non-darcy flow equations are showed in two general ways including: and .one of the main parameters for flo...

In this paper we consider a modification to Darcy equation by taking into account the dependence of viscosity on the pressure. We present a stabilized mixed formulation for the resulting governing equations. Equal-order interpolation for the velocity and pressure is considered, and shown to be stable (which is not the case under the classical mixed formulation). The proposed mixed formulation i...

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...

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...

We consider a model for flow in a porous medium with a fracture in which the flow in the fracture is governed by the Darcy-Forchheimer law while that in the surrounding matrix is governed by Darcy’s law. We give an appropriate mixed, variational formulation and show existence and uniqueness of the solution. To show existence we give an analogous formulation for the model in which the Darcy-Forc...

The subject of this paper is a first-order system least-squares formulation for the Stokes equation which remains uniformly valid in the limit of vanishing viscosity. For this so-called Darcy-Stokes flow problem we establish continuity and coercivity of the corresponding least-squares functional in appropriate norms. Two types of finite element spaces for the approximation of the velocity field...

the consolidation test method proposed by terzaghi and used in most soil mechanic laboratories has limitations and weaknesses. to get correct results, improvement and modification of the test method is essential. several experimental methods, such as constant loading rate, gradient and constant rate of strain (crs) have been used over the past 40 years. of these methods, crs is more advantageou...

This paper presents the lowest-order weak Galerkin finite element method for solving the Darcy equation on quadrilateral and hybrid meshes consisting of quadrilaterals and triangles. In this approach, the pressure is approximated by constants in element interiors and on edges. The discrete weak gradients of these constant basis functions are specified in local Raviart-Thomas spaces RT[0] for qu...