To simulate flows around solid obstacles of complex geometries, various immersed boundary methods had been developed. Their main advantage is the efficient implementation for stationary or moving solid boundaries of arbitrary complexity on fixed non-body conformal Cartesian grids. The Brinkman penalization method was proposed for incompressible viscous flows by penalizing the momentum equations...

This paper presents a new approach to verify accuracy of computational simulations. We develop mathematical theorems which can serve as robust a posteriori error estimation techniques to identify numerical pollution, check the performance of adaptive meshes, and verify numerical solutions. We demonstrate performance of this methodology on problems from flow thorough porous media. However, one c...

We present an unconditionally energy stable and uniquely solvable finite difference scheme for the Cahn-Hilliard-Brinkman (CHB) system, which is comprised of a Cahn-Hilliard-type diffusion equation and a generalized Brinkman equation modeling fluid flow. The CHB system is a generalization of the Cahn-Hilliard-Stokes model and describes two phase very viscous flows in porous media. The scheme is...

A global nonlinear stability analysis is performed for a couple-stress fluid layer heated from below saturating a porous medium with temperature-pressure dependent viscosity for different conducting boundary systems. Here, the global nonlinear stability threshold for convection is exactly the same as the linear instability boundary. This optimal result is important because it shows that lineari...

The paper numerically presents laminar forced convection of a nanofluid flowing in a duct at microscale. Results were compared with both analytical and experimental data and observed good concordance with previous studies available in the literature. Influences of Brinkman and Reynolds number on thermal and hydrodynamic indexes have been investigated. For a given nanofluid, no change in efficie...

In this paper, we obtain the continuous dependence and convergence results for the Brinkman and Forchheimer coefficients of a differential equation that models the flow of fluid in a saturated porous medium.

We performed a cross-sectional study that included 100 HIV-infected Japanese men without hemophilia to examine the influence of smoking on HIV infection. History of smoking was obtained using a questionnaire. The percentage of current smokers was 40 % and was the highest (50 %) among men in their forties. The mean Brinkman index (BI, number of cigarettes smoked per day multiplied by years of sm...

In this paper, we use Stokes, Brinkman and Darcy equations to approximate the porous continuum media of ligament tissues respectively, simulate the flow field with FLUENT software, and study the shear stress on the cell surface due to the interstitial fluid flow. Since the Brinkman equation approaches Stokes equation well in high hydraulic permeability (k p) condition (k p ≥1.0×10(-8) m(2) in o...

In this paper, we consider 2D and 3D Darcy-Stokes interface problems. These equations are related to Brinkman model that treats both Darcy’s law and Stokes equations in a single form of PDE but with strongly discontinuous viscosity coefficient and zerothorder term coefficient. We present three different methods to construct uniformly stable finite element approximations. The first two methods a...

The effects of smoking and age on the results of hematologic tests were determined in a group of 429 healthy male workers. The results obtained were as follows: 1) The values of total leucocyte count (x10(9)/l), neutrophil count (x10(9)/l), lymphocyte count (x10(9)/l), monocyte count (x10(9)/l), hemoglobin (g/l), hematocrit, mean corpuscular volume (MCV; fl), mean corpuscular hemoglobin (MCH; p...