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...

In this report, a partitioned time stepping algorithm which allows different time steps in the fluid region and the porous region is analyzed for the fully evolutionary Stokes-Darcy problem. This method requires only one, uncoupled Stokes and Darcy sub-physics and sub-domain solve per time step. Under a modest time step restriction of the form 4t ≤ C where C = C(physical parameters) we prove ze...

In this report, a partitioned time stepping algorithm for transient flow in a porous medium coupled to a free flow in embedded conduits is analyzed. The coupled flow is modeled by the fully evolutionary Stokes-Darcy problem. This method requires only solve one, uncoupled Stokes and Darcy sub-physics and subdomain per time step. On the interface between the matrix and conduit, Beavers-Joseph int...

This paper presents a finite volume discretization of two-phase Darcy flows in discrete fracture networks taking into account the mass exchange between the matrix and the fracture. We consider the asymptotic model for which the fractures are represented as interfaces of codimension one immersed in the matrix domain, leading to the so called hybrid dimensional Darcy flow model. The pressures at ...

The project in memory of anthropologist, writer and politician Darcy Ribeiro is analyzed, with emphasis on the relationship he had with his personal archives and the creation of the Darcy Ribeiro Foundation, established to give continuity to his 'legacy.' It highlights the influences present in the formation of his archive and presents an ethnography that seeks to restore the historicity of the...

This paper presents a two-grid method for solving systems of partial differential equations modelling free flow coupled with porous media flow. This work considers both the coupled Stokes and Darcy as well as the coupled Navier-Stokes and Darcy problems. The numerical schemes proposed are based on combinations of the continuous finite element method and the discontinuous Galerkin method. Numeri...

Gas reservoirs with low permeability (k<0.1 mD) are among the unconventional reservoirs and are commonly termed as "Tight Gas Reservoirs". In conventional gas reservoirs that have high permeability, the flow of gas is basically controlled by the reservoir permeability and it is calculated using the Darcy equation. In these reservoirs, gas flow due to gas diffusion is ignored compared to Dar...

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...

Simulations were carried out using penalty finite element analysis with bi-quadratic elements to investigate the influence of uniform and non-uniform heating of bottom wall within a trapezoidal enclosure of various inclination angles ðuÞ. Parametric study has been carried out for a wide range of Rayleigh number ðRaÞ ð10 6 Ra 6 10Þ, Prandtl number ðPrÞ ð0:026 6 Pr 6 988:24Þ and Darcy number ðDaÞ...