In this article we investigate the numerical approximation of the Darcy equations in an axisymmetric domain, subject to axisymmetric data. Rewriting the problem in cylindrical coordinates reduces the 3-D problem to a problem in 2-D. This reduction to 2-D requires the numerical analysis to be studied in suitably weighted Hilbert spaces. In this setting the Raviart-Thomas (RT) and Brezzi-Douglas-...

As a first draft of a model for a river flowing on a homogeneous porous ground, we consider a system where the Darcy and Stokes equations are coupled via appropriate matching conditions on the interface. We propose a discretization of this problem which combines the mortar method with standard finite elements, in order to handle separately the flow inside and outside the porous medium. We prove...

In this article we investigate the numerical approximation of coupled Stokes and Darcy fluid flow equations in an axisymmetric domain. The fluid flow is assumed to be axisymmetric. Rewriting the problem in cylindrical coordinates reduces the 3-D problem to a problem in 2-D. This reduction to 2-D requires the numerical analysis to be studied in suitably weighted Hilbert spaces. In this setting w...

We propose and analyze a partitioned numerical method for the fully evolutionary Stokes-Darcy equations that model the coupling between surface and groundwater flows. The proposed method uncouples the surface from the groundwater flow by using the implicit-explicit combination of the Crank-Nicolson and Leapfrog methods for the discretization in time with added stabilization terms. We prove that...

Starting from the non-stable P1=P0 discretization we build enhanced methods for the Darcy equation which are stable and locally mass-conservative. The methods are derived in a Petrov–Galerkin framework where both velocity and pressure trial spaces are enriched with multiscale functions. These functions solve local problems correcting the residuals of the strong equations in each element and int...

The paper provides a numerical investigation of the entropy generation analysis due to natural convection in an inclined square porous cavity. The coupled equations of mass, momentum, energy and species conservation are solved using the Control Volume Finite-Element Method. Effect of medium permeability and inclination angle on entropy generation is analysed. It was found that according to the ...

We investigate the nature of entropy generation for natural convection in a twodimensional square section enclosure vibrating sinusoidally perpendicular to the applied temperature gradient in a zero-gravity field. The enclosure is assumed to fill with porous media. The Darcy momentum equation is used to model the porous media. The full governing differential equations are simplified with the Bo...

Unsteady mixed convection flows in a lid-driven square cavity filled with a fluid-saturated porous medium is investigated numerically. The two vertical walls of the enclosure are insulated while the bottom wall is cooled. The top wall is heated sinusoidally and moving at a constant speed. The governing equations are solved numerically by using finite volume method with SIMPLE algorithm. The res...

We propose an efficient iterative method to solve the mixed Stokes-Dracy model for coupling fluid and porous media flow. The weak formulation of this problem leads to a coupled, indefinite, ill-conditioned and symmetric linear system of equations. We apply a decoupled preconditioning technique requiring only good solvers for the local mixed-Darcy and Stokes subproblems. We prove that the method...

Numerical solutions using finite element methods are considered for transient flow in a porous medium coupled to free flow in embedded conduits. Such situations arise, for example, for groundwater flows in karst aquifers. The coupled flow is modeled by the Darcy equation in a porous medium and the Stokes equations in the conduit domain. On the interface between the matrix and conduit, Beavers–J...