We investigate 3-dimensional motility of sperm in fluids with a sparse network of stationary obstacles or fibers. The Brinkman equation is used to model the average fluid flow where a resistance term is inversely proportional to the permeability of the porous medium and represents the effect due to the presence of the fibers. The sperm flagellum is idealized as a Kirchhoff rod that can exhibit ...

We study the interaction between a poroelastic medium and a fracture filled with fluid. The flow in the fracture is described by the Brinkman equations for an incompressible fluid and the poroelastic medium by the quasi-static Biot model. The two models are fully coupled via the kinematic and dynamic conditions. The Brinkman equations are then averaged over the cross-sections, giving rise to a ...

This paper discusses a numerical subgrid resolution approach for solving the Stokes-Brinkman system of equations, which is describing coupled flow in plain and in highly porous media. Various scientific and industrial problems are described by this system, and often the geometry and/or the permeability vary on several scales. A particular target is the process of oil filtration. In many complic...

Abstract We investigate the effects of anisotropic permeability and changing boundary conditions upon onset penetrative convection in a porous medium Darcy type Brinkman type. Attention is focussed on critical eigenfunctions which show how many cells will be found layer. The number shown to depend critically ratio vertical horizontal permeability, coefficient, upper condition for velocity may D...

The Brinkman model describes flow of fluid in complex porous media with a high-contrast permeability coefficient such that the flow is dominated by Darcy in some regions and by Stokes in others. A weak Galerkin (WG) finite element method for solving the Brinkman equations in two or three dimensional spaces by using polynomials is developed and analyzed. The WG method is designed by using the ge...

A solid tumor is investigated as porous media for fluid flow simulation. Most of the studies use Darcy model for porous media. In Darcy model, the fluid friction is neglected and a few simplified assumptions are implemented. In this study, the effect of these assumptions is studied by considering Brinkman model. A multiscale mathematical method which calculates fluid flow to a solid tumor is us...

A local interpolation operator, preserving the divergence, is constructed explicitly, which is the first ever one for the divergence-free elements. A divergence-free finite element method is applied to the Darcy-Stokes-Brinkman flow in a mixed region of both free and porous medium. The method is of optimal order in contrast to the traditional H and H mixed finite elements, which work for either...

A numeriea! investigation for forced convection in a constant-temperaJure parallel pkue channel wilh porous cavity and block alternately emplaced on lhe bottom plaJe is presented in this work. The Brinkman-Forchheimer-extended Darcy mode~ whil:h accounts for the effects of impermeable boundary and inertia, is used to characterize the flow field inside the porous region. Solutions of Ihe coupled...