We prove continuous dependence of solutions of the Brinkman–Forchheimer equations on the Brinkman and Forchheimer coefficients in H1 norm. c © 2005 Elsevier Ltd. All rights reserved.

Non-Darcy behavior is important for describing fluid flow in porous media in situations where high velocity occurs. A criterion to identify the beginning of non-Darcy flow is needed. Two types of criteria, the Reynolds number and the Forchheimer number, have been used in the past for identifying the beginning of non-Darcy flow. Because each of these criteria has different versions of definition...

Generalized Forchheimer equations. The generalized Forchheimer equations are introduced to describe more complex regimes of luid lows in porous media when Darcy's law becomes inadequate. Although widely acknowledged in engineering, the Forchheimer equations still do not have as much mathematical analysis as Darcy's law. This is partly due to the dif iculty lying in their genuine nonlinearity. I...

We study the generalized Forchheimer equations for slightly compressible fluids in porous media. The structural stability is established with respect to either the boundary data or the coefficients of the Forchheimer polynomials. An inhomogeneous Poincare-Sobolev inequality related to the non-linearity of the equation is used to study the asymptotic behavior of the solutions. Moreover, we prove...

The numerical prediction of channel segregations during two-dimensional columnar solidification of Sn-Pb alloy is analyzed when inertia is considered in the dendritic mushy zone. This contribution is included in the momentum transport equation through the quadratic Forchheimer correction term. A significant influence of the Forchheimer term in the vicinity of the liquidus region is found. The n...

The present analysis investigates non-Darcy forced convective heat transfer in a channel confined by two parallel walls subjected to uniform heat flux in a highly porous medium saturated with a non-Newtonian power-law fluid. Extensive numerical integrations have been carried out utilizing the Brinkman-Forchheimer extension of the Darcy model in order to study the effects of pseudoplasticity, an...

We prove the existence of regular dissipative solutions and global attractors for the 3D Brinkmann-Forchheimer equations with the nonlinearity of an arbitrary polynomial growth rate. In order to obtain this result, we prove the maximal regularity estimate for the corresponding semi-linear stationary Stokes problem using some modification of the nonlinear localization technique. The applications...

We consider a model for flow in a porous medium with a fracture in which the flow in the fracture is governed by the Darcy-Forchheimer law while that in the surrounding matrix is governed by Darcy’s law. We give an appropriate mixed, variational formulation and show existence and uniqueness of the solution. To show existence we give an analogous formulation for the model in which the Darcy-Forc...

An efficient nonlinear multigrid method for a mixed finite element method of the Darcy-Forchheimer model is constructed in this paper. A Peaceman-Rachford type iteration is used as a smoother to decouple the nonlinearity from the divergence constraint. The nonlinear equation can be solved element-wise with a closed formulae. The linear saddle point system for the constraint is reduced into a sy...

SONG, H. and TAO, L., 2007. Homotopy analysis of 1D unsteady, nonlinear groundwater flow through porous media. Journal of Coastal Research, SI 50 (Proceedings of the 9th International Coastal Symposium), pg – pg. Gold Coast, Australia, ISBN 1-891276-54-9 In this paper, the 1D unsteady, nonlinear groundwater flow through porous media, corresponding to flood in an aquifer between two reservoirs, ...