A three-dimensional boundary layer solution is presented to study the effect of magneto-hydrodynamic with variable viscosity on natural convection in the vicinity of an axisymmetric stagnation point on heated vertical surfaces saturated in porous medium. The fluid viscosity is assumed to vary as a linear function of temperature. The governing partial differential equations for the flow and heat...

We propose and analyze a third-order in time numerical algorithm for the Stokes-Darcy system for flows in fluid saturated karst aquifers. A novel third-order Adams-Moulton scheme is used for the discretization of the dissipative term while a third-order explicit Adams-Bashforth scheme is utilized for the time discretization of the interface term. The scheme is efficient in the sense that one ne...

We propose a novel second order in time, decoupled and unconditionally stable numerical scheme for solving the Cahn-Hilliard-Darcy (CHD) system which models two-phase flow in porous medium or in a Hele-Shaw cell. The scheme is based on the ideas of second order convex-splitting for the Cahn-Hilliard equation and pressure-correction for the Darcy equation. We show that the scheme is uniquely sol...

The Brinkman model is a unified law governing the flow of a viscous fluid in cavity (Stokes equations) and in porous media (Darcy equations). In this work, we explore a novel mixed formulation of the Brinkman problem by introducing the flow’s vorticity as an additional unknown. This formulation allows for a uniformly stable and conforming discretization by standard finite element (Nédélec, Ravi...

The goal of this work is to predict reasonable lifetime of a filter used to remove debris (e.g. foreign particles and gels) from the melt stream of an extrusion process. We are developing models which incorporate nonNewtonian porous media flow through a medium whose porosity changes as debris accumulates. Boundary conditions are based on the assumption of constant flow rate and coupling with ot...

The effect of non-uniform heat generation on an unsteady MHD laminar boundary layer flow of viscous, incompressible fluid over a vertical stretching plate embedded in a sparsely packed porous medium is investigated numerically. The flow in the porous medium is governed by Brinkman-Forchheimer extended Darcy model. The variation of porosity, permeability and thermal conductivity is assumed. By a...

We describe multiscale mortar mixed finite element discretizations for second order elliptic and nonlinear parabolic equations modeling Darcy flow in porous media. The continuity of flux is imposed via a mortar finite element space on a coarse grid scale, while the equations in the coarse elements (or subdomains) are discretized on a fine grid scale. We discuss the construction of multiscale mo...

The modelling of natural convection in porous media is receiving increased interest due to its significance environmental and engineering problems. State-of-the-art simulations are based on the classic macroscopic Darcy–Oberbeck–Boussinesq (DOB) equations, which widely accepted capture underlying physics provided Darcy number, $Da$ , small. In this paper we analyse extend recent pore-resolved d...

Linear stability of double diffusive convection of Darcy-Maxwell fluid with Soret and Dufour effects is investigated. The effects of the Soret and Dufour numbers, Lewis number, relaxation time and solutal Darcy Rayleigh number on the stationary and oscillatory convection are presented graphically. The Dufour number enhances the stability of Darcy-Maxwell fluid for stationary convection while it...

In the present work, forced convection heat transfer of slip flow in porous micro-tubes with local thermal non-equilibrium between the gas and the solid matrix is investigated numerically. For this purpose, the flow is considered hydrodynamically developed but thermally developing. The Darcy-Brinkman-Forchheimer model in conjunction with separate energy equations for the gas and the solid matri...