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...

Many microorganisms swim in a highly heterogeneous environment with obstacles such as fibers or polymers. To better understand how this environment affects microorganism swimming, we study propulsion of a cylinder or filament in a fluid with a sparse, stationary network of obstructions modeled by the Brinkman equation. The mathematical analysis of swimming speeds is investigated by studying an ...

Numerical and analytical solutions of Stokes theory couple stress fluid under the effects constant, space, variable viscosity in inclined channel are discussed here. The considered is described mathematically with definition tensor. dimensional form boundary value problem transformed into dimensionless by defining quantities then solved help perturbation technique. expressions velocity temperat...

We present a well-posed model for the Stokes/Brinkman problem with a family of jump embedded boundary conditions (J.E.B.C.) on an immersed interface with weak regularity assumptions. It is issued from a general framework recently proposed for fictitious domain problems. Our model is based on algebraic transmission conditions combining the stress and velocity jumps on the interface S separating ...

We introduce a new finite element method for the approximation of the three-dimensional Brinkman problem formulated in terms of the velocity, vorticity, and pressure fields. The proposed strategy exhibits the advantage that, at the continuous level, a complete decoupling of vorticity and pressure can be established under the assumption of sufficient regularity. The velocity is then obtained as ...

Effects of the bounding solid walls are examined numerically for slow flow over regular, square arrays of circular cylinders between two parallel plates. A local magnitude of the rate of entropy generation is used effectively to determine the flow region affected by the presence of the solid boundary. Computed axial pressure gradients are compared to the corresponding solution based on the Darc...

Among the motions of a fluid over a plane wall, the Stokes’ problems as well as the motion induced by a constantly accelerating plate have been extensively studied in the literature. However, the first closed-form solutions for the motion of a viscous fluid over an oscillating plate have been late enough obtained by Erdogan [1]. These solutions, as well as those corresponding to the fluid motio...

<p style='text-indent:20px;'>This paper presents a hybridized weak Galerkin (HWG) finite element method for solving the Brinkman equations. Mathematically, equations can model Stokes and Darcy flows in unified framework so as to describe fluid motion porous media with fractures. Numerical schemes equations, therefore, must be designed tackle at same time. We demonstrate that HWG is capabl...

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...