The problem of hydrodynamic dispersion in non-Darcy free convection heat and mass transfer from vertical surface embedded in a porous medium has been presented. The Forchheimer extension is considered in the flow equations. The flow, temperature and concentration fields in Darcy and non-Darcy porous media are observed to be governed by complex interactions among the diffusion rate Le, buoyancy ...

There has been a surge of work on models for coupling surface-water with groundwater flows which is at its core the Stokes-Darcy problem. The resulting (Stokes-Darcy) fluid velocity is important because the flow transports contaminants. The analysis of models including the transport of contaminants has, however, focused on a quasi-static Stokes-Darcy model. Herein we consider the fully evolutio...

The infinite Darcy-Prandtl number model is an effective reduced model for describing convection in a fluid-saturated porous medium. It is well known that the deterministic model does not possess a unique invariant measure. In this work we study the dynamics of the infinite Darcy-Prandtl number model, under an additive stochastic forcing of its low modes. This is the so-called stochastic infinit...

This paper deals with the finite element approximation of Darcy–Brinkman- Forchheimer equation, involving a porous media spatially-varying porosity, mixed boundary condition such as inhomogeneous Dirichlet and traction conditions. We first prove that considered problem has unique solution if source terms are small enough. The convergence Taylor–Hood using interpolation porosity is then proved u...

This paper presents a new approach to verify accuracy of computational simulations. We develop mathematical theorems which can serve as robust a posteriori error estimation techniques to identify numerical pollution, check the performance of adaptive meshes, and verify numerical solutions. We demonstrate performance of this methodology on problems from flow thorough porous media. However, one c...

Cocurrent spontaneous imbibition (COCSI) of an aqueous phase into matrix blocks arising from capillary forces is an important mechanism for petroleum recovery from fractured petroleum reservoirs. In this work, the modeling of countercurrent imbibition is used to develop the appropriate scaling equations. Considering the imbibition process and the water and oil movement respectively as the wet p...

Abstract. In reservoir simulations, nearwell regions usually require finer space and time scales compared with the remaining of the reservoir domain. We present a domain decomposition algorithm for a two phase Darcy flow model coupling nearwell regions locally refined in space and time with a coarser reservoir discretization. The algorithm is based on an optimized Schwarz method using a full ov...

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...

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...