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...

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...

We study the existence of weak solutions to a mixture model for tumour growth that consists of a Cahn–Hilliard–Darcy system coupled with an elliptic reactiondiffusion equation. The Darcy law gives rise to an elliptic equation for the pressure that is coupled to the convective Cahn–Hilliard equation through convective and source terms. Both Dirichlet and Robin boundary conditions are considered ...

Domain decomposition methods for solving the coupled Stokes-Darcy system with the Beavers-Joseph interface condition are proposed and analyzed. Robin boundary conditions are used to decouple the Stokes and Darcy parts of the system. Then, parallel and serial domain decomposition methods are constructed based on the two decoupled sub-problems. Convergence of the two methods is demonstrated and t...

The Flow through saturated-unsaturated porous media is extremely important in various natural and industrial based applications. While the Darcy's law with various modifications are used to model the flow through a porous media, the flow through unsaturated porous media is largely based on conservation of mass and modified Darcy's law where non-linear relationship exists between the p...

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...

This paper presents studies on applying the novel weak Galerkin finite element method (WGFEM) to a two-phase model for subsurface flow, which couples the Darcy equation for pressure and a transport equation for saturation in a nonlinear manner. The coupled problem is solved in the framework of operator decomposition. Specifically, the Darcy equation is solved by theWGFEM, whereas the saturation...

Hybrid or multiphysics algorithms provide an efficient computational tool for combining microand macroscale descriptions of physical phenomena. Their use becomes imperative when microscale descriptions are too computationally expensive to be conducted in the whole domain, while macroscale descriptions fail in a small portion of the computation domain. We present a hybrid algorithm to model a ge...

Hall effects on an unsteady MHD flow of a viscous incompressible electrically conducting fluid between two rotating disks with non-coincident parallel axes embedded in a porous medium have been studied. The governing equations have been solved analytically using the Laplace transform technique. The effects of rotation parameter, Hall parameter, Hartmann number and Darcy number have been conside...

We consider finite element methods for the Darcy equations that are designed to work with standard, low order C finite element spaces. Such spaces remain a popular choice in the engineering practice because they offer the convenience of simple and uniform data structures and reasonable accuracy. A consistently stabilized method [20] and a least-squares formulation [18] are compared with two new...