Related papers: A Multiscale Model of Partial Melts 2: Numerical R…
This paper is devoted to the homogenization of the heat conduction equation, with a homogeneous Dirichlet boundary condition, having a periodically oscillating thermal conductivity and a vanishing volumetric heat capacity. A homogenization…
The work is devoted to the development and computational implementation of the homogenization method for modeling unsteady flows of a viscous incompressible fluid in periodic porous media taking into account memory effects. At the…
Asymptotic multiple scale homogenisation allows to determine the effective behaviour of a porous medium by starting from the pore-scale description, when there is a large separation between the pore-scale and the macroscopic scale. When the…
We prove explicit estimates for the error in random homogenization of degenerate, second-order Hamilton-Jacobi equations, assuming the coefficients satisfy a finite range of dependence. In particular, we obtain an algebraic rate of…
This study proposes a multi-field asymptotic homogenization for the analysis of thermo-piezoelectric materials with periodic microstructures. The effect of the microstructural heterogeneity is taken into account by means of periodic…
This paper presents a new homogenized model of two-component electrolyte transport through a weakly piezoelectric porous medium. The model relevant to the microscopic scale describes quasi-stationary states of the medium while reflecting…
In this paper a new primal-dual mixed finite element method is introduced, aimed to model multiscale problems with several geometric subregions in the domain of interest. In each of these regions porous media fluid flow takes place, but…
Inspired by applications, we study the effect of interface slip on the effective wave propagation in poroelastic composites. The current literature on the homogenization for the poroelastic wave equations are all based on the no-slip…
In this paper, we present a general derivation of multicontinuum equations and discuss cell problems. We present constraint cell problem formulations in a representative volume element and oversampling techniques that allow reducing…
The paper presents a new type of weakly nonlinear two-scale model of controllable periodic porous piezoelectric structures saturated by Newtonian fluids. The flow is propelled by peristaltic deformation of microchannels which is induced due…
This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods…
In this article we are interested in quantitative homogenization results for linear elliptic equations in the non-stationary situation of a straight interface between two heterogenous media. This extends the previous work [Josien, 2019] to…
A method of modelling the three-dimensional microstructure of random isotropic two-phase materials is proposed. The information required to implement the technique can be obtained from two-dimensional images of the microstructure. The…
This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable…
This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order…
In this work we present a mass conservative numerical scheme for two-phase flow in porous media. The model for flow consists on two fully coupled, non-linear equations: a degenerate parabolic equation and an elliptic equation. The proposed…
We study the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable layer (e.g., bedrock).…
We consider the homogenization problem for the stochastic porous-medium type equation $\p_{t} u^\epsilon =\Delta f\left(T\left(\frac{x}{\ep}\right)\om,u^\ep\right)$, with a well-prepared initial datum, where $f(T(y)\om,u)$ is a stationary…
We investigate the influence of multiscale aggregation and deposition on the colloidal dynamics in a saturated porous medium. At the pore scale, the aggregation of colloids is modeled by the Smoluchowski equation. Essentially, the colloidal…
We investigate volume-element sampling strategies for the stochastic homogenization of particle-reinforced composites and show, via computational experiments, that an improper treatment of particles intersecting the boundary of the…