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...

Abstract We study a system of parabolic equations consisting double nonlinear equation Forchheimer type coupled with semilinear equation. The describes fluid-like driven for active-passive pedestrian dynamics. structure the nonlinearity coupling allows us to prove uniqueness solutions. provide also stability estimate solutions respect selected parameters.

A numerical model is presented for computation of unsteady two-fluid interfaces in nonlinear porous media flow. The nonlinear Forchheimer equation is included in the Navier-Stokes equations for porous media flow. The model is based on capturing the interface on a fixed mesh domain. The zero level set of a pseudo-concentration function, which defines the interface between the two fluids, is gove...

Three dimensional heat transfer and water flow characteristic in a set of rectangular microchannel heat sinks for advanced electronic systems investigated in this paper. The full Navier-Stoke’s approach is employed for this kind of narrow channels for the water flow assessments. The complete form of the energy equation accompanying the dissipation terms is also linked to the momentum equations....

Many important natural processes involving flow through porous media are characterized by large filtration velocity. Therefore, it is important to know when the transition from viscous to the inertial flow regime actually occurs in order to obtain accurate models for these processes. In this paper, a detailed computational study of laminar and inertial, incompressible, Newtonian fluid flow acro...

This paper presents a Buckley-Leverett analytical solution for non-Darcy displacement of two immiscible fluids in porous media. The multiphase non-Darcy displacement is described using a Forchheimer equation or other non-Darcy flow correlations under multiphase flow conditions. The analytical solution is used to obtain some insight into the physics of displacement involving non-Darcy flow effec...

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...