In this paper, we carry out an a posteriori error analysis of Legendre spectral approximations to the Stokes/Darcy coupled equations. The spectral approximations are based on aweak formulation of the coupled equations by using the Beavers-JosephSaffman interface condition. The main contribution of the paper consists of deriving a number of posteriori error indicators and their upper and lower b...

Abstract A priori bounds were derived for the flow in a bounded domain viscous-porous interfacing fluids. We assumed that viscous fluid was slow $\Omega _{1}$ Ω 1 , which governed by Boussinesq equations. For porous medium _{2}$ 2 we supposed satisfied ...

Steady state natural convection of Al2O3-water nanofluid inside a square cavity filled with a porous medium is investigated numerically. The temperatures of the two side walls of the cavity are maintained at TH and TC, where TC has been considered as the reference condition. The top and the bottom horizontal walls have been considered to be insulated i.e., non-conducting and impermeable to mass...

In this article, we analyze the flow of a fluid through a domain modeled using the equations for generalized non-linear Stokes flow coupled with flow through a porous media, modeled using generalized non-linear Darcy flow equations. A prescribed flow rate is assumed specified along the inflow portion of the non-linear Stokes flow boundary. Existence and uniqueness of a variational solution to t...

Analytical solutions are derived for a pressure transmission experiment of a saturated charged compressible porous medium. The governing equations describe infinitesimal deformations of charged porous media saturated with a mono-valent ionic solution. From the governing equations a coupled diffusion equation in state space notation is derived for the electro-chemical potentials, which is decoup...

The transport of substances back and forth between surface water and groundwater is a very serious problem. We study herein the mathematical model of this setting consisting of the Stokes equations in the fluid region coupled with the Darcy equations in the porous medium, coupled across the interface by the Beavers–Joseph–Saffman conditions. We prove existence of weak solutions and give a compl...

We study the mixed formulation of the stochastic Hodge–Laplace problem defined on an n-dimensional domain D (n 1), with random forcing term. In particular, we focus on the magnetostatic problem and on the Darcy problem in the three-dimensional case. We derive and analyse the moment equations, that is, the deterministic equations solved by the mth moment (m 1) of the unique stochastic solution o...

In this paper we study interface equations associated to the Darcy-Stokes problem 8 using the classical Steklov-Poincaré approach and a new one called augmented. We compare 9 these two families of methods and characterize at the discrete level suitable preconditioners 10 with additive and multiplicative structures. Finally, we present some numerical results to as11 sess their behavior in presen...

Abstract—This paper presents the heat and mass driven natural convection succession in a Darcy thermally stratified porous medium that embeds a vertical semi-infinite impermeable wall of constant heat flux and concentration. The scale analysis of the system determines the two possible maps of the heat and mass driven natural convection sequence along the wall as a function of the process parame...

Effective numerical simulation of many EOR problems requires very accurate approximation of the Darcy velocities of the respective fluids. In this paper we describe a new method for the accurate determination of the Darcy velocity of the total fluid in the miscible displacement of one incompressible fluid by another in a porous medium. The new mixed finite-element procedure solves for both the ...