We consider the influence of heat losses through the walls of a Hele-Shaw cell on the linear stability and nonlinear dynamics of exothermic chemical fronts whose solutal and thermal contributions to density changes have the same signs. Our analysis is based on the reaction-diffusion-convection equations obtained from the Darcy-Boussinesq approximation. The parameters governing the equations are...

The spline element method with constraints is a discretization method where the unknowns are expanded as polynomials on each element and Lagrange multipliers are used to enforce the interelement conditions, the boundary conditions and the constraints in numerical solution of partial differential equations. Spaces of piecewise polynomials with global smoothness conditions are known as multivaria...

The present work investigates the effect of vertical harmonic vibration on the onset of convection in an infinite horizontal layer of a binary fluid mixture saturating a porous medium. We assume that the fluid component of the mixture is viscous and incompressible, the porous medium is homogeneous and isotropic, and the boundaries are rigid and impermeable, with slip allowed. A constant tempera...

Homogenization techniques are used to derive a double porosity model for single phase flow in a reservoir with a preferred direction of fracture. The equations in the microscopic model are the usual ones derived from Darcy’s law in the fractures and matrix (rock). The permeability coefficients over the matrix domain are scaled, using a parameter ε, based on the fracture direction in the reservo...

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. Introducing the flow’s vorticity as additional unknown, this formulation allows for a uniformly stable and conforming discretization by standard finite elements (Nédélec, Raviart-...

We study the mixed formulation of the stochastic Hodge-Laplace problem defined on a 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 analyze the moment equations, that is the deterministic equations solved by the m-th moment (m ≥ 1) of the unique stochastic solutio...

In a system where a free fluid flow is coupled to flow in a porous medium, different PDEs are solved simultaneously in two subdomains. We consider steady Stokes equations in the free region, coupled across a fixed interface to Darcy equations in the porous substrate. In this paper, the numerical solution is obtained using the boundary integral formulation with regularized Green’s function. High...

Diffused pneumatic silencer has been widely used in pneumatic fields because of its small dimensions and high performance on noise reduction. Numerical simulation of its interior and exterior flow field is important to studying the gas flow in the silencer and the flow structure outside the silencer, understanding the mechanism of its noise reduction. Porous media model and Darcy-Forchheimer pr...

The Soret and Dufour effects on the steady, laminar mixed convection heat and mass transfer along a semi-infinite vertical plate embedded in a micropolar fluid saturated non-Darcy porous medium with heat and mass flux conditions are investigated. The non-linear governing equations and their associated boundary conditions are initially cast into dimensionless forms using similarity transformatio...

This paper presents an incompressible two-dimensional heat and mass transfer of an electrically conducting micropolar fluid flow in a porous medium between two parallel plates with chemical reaction, Hall and ion slip effects. Let there be periodic injection or suction at the lower and upper plates and the nonuniform temperature and concentration at the plates are varying periodically with time...