In this paper, the asymptotic homogenization method is applied to the filtration theory of a
generalized Newtonian fluid in periodic porous media. The asymptotic expansion of non …

In this study, we numerically investigated the forced heat-transfer and laminar flow in a two-
dimensional microchannel whose lower half was filled with a porous medium. The …

This research is devoted to the mathematical modeling for the filtration of a generalized
Newtonian fluid in porous media by applying the homogenization method. The so-called …

The two key parameters of the Brinkman's model for fluid flow in porous media—
permeability and effective viscosity—are determined theoretically. The analytical solution of …

This paper presents a determination of the effective viscosity in the Brinkman equation by a
numerical simulation of an imaginary physical experiment with a viscometer. The model of a …

A new approximate approach to solve the two-dimensional boundary-value problems for the
Stokes flows in a porous medium composed of a set of circular inclusions is proposed. The …

A multiscale finite element method based on the bubble functions is used to generate stable
and accurate solutions for the diffusion-reaction equation for both dissipation and production …

A space–time finite element discretization method for unsteady transport phenomena is
formulated using a variational multiscale finite element scheme. The described discretization …

Due to the multi-scale nature of the convection–diffusion equation the standard Galerkin
method fails to predict accurate and stable results. A multi-scale finite element method …

Fourier series multiscale method, a concise and efficient analytical approach for multiscale
computation, will be developed out of this series of papers. In the sixth paper, exact analysis …