<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In the paper, generalized boundary conditions were used for the homogenization of coefficients of the Laplace partial differential equation in the context of Darcy flow and heat diffusion phenomena. The mesoscopic boundary value problem was defined and analyzed from the variational perspective and the finite element formulation of the homogenization problem was provided. The matrix equation for the apparent macroscopic properties, resulting from FEM discretization, was derived and utilized in two illustrative examples: homogenization of the filtration coefficient of clay amended with expanded shale and thermal conductivity of the soil with multiple fractions. It is shown, that generalized boundary conditions can provide very good homogenization results without the assumption of the periodicity of the material. For best results, the microscopic length parameter has to be properly estimated.</p>
</abstract>

In the paper, generalized boundary conditions were used for the homogenization of coefficients of the Laplace partial differential equation in the context of Darcy flow and heat diffusion phenomena. The mesoscopic boundary value problem was defined and analyzed from the variational perspective and the finite element formulation of the homogenization problem was provided. The matrix equation for the apparent macroscopic properties, resulting from FEM discretization, was derived and utilized in two illustrative examples: homogenization of the filtration coefficient of clay amended with expanded shale and thermal conductivity of the soil with multiple fractions. It is shown, that generalized boundary conditions can provide very good homogenization results without the assumption of the periodicity of the material. For best results, the microscopic length parameter has to be properly estimated.

Application of generalized boundary conditions for homogenization of thermal and filtration properties of soils

Studia Geotechnica et Mechanica

This work is licensed under the Creative Commons Attribution 4.0 International License.

In the paper, generalized boundary conditions were used for the homogenization of coefficients of the Laplace partial differential equation in the context of...

Application of generalized boundary conditions for homogenization of thermal and filtration properties of soils

Article Category: Special Issue 19th KKMGiIG

Publicado en línea: 30 nov 2023

Páginas: 362 - 369

Recibido: 28 feb 2023

Aceptado: 21 ago 2023

DOI: https://doi.org/10.2478/sgem-2023-0025

Palabras clave
Homogenization, Finite element method, Generalized boundary conditions, Darcy flow, Heat conduction

© 2023 Marek Wojciechowski, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Application of generalized boundary conditions for homogenization of thermal and filtration properties of soils

Article Category: Special Issue 19th KKMGiIG

Publicado en línea: 30 nov 2023

Páginas: 362 - 369

Recibido: 28 feb 2023

Aceptado: 21 ago 2023

DOI: https://doi.org/10.2478/sgem-2023-0025

Palabras claveHomogenization, Finite element method, Generalized boundary conditions, Darcy flow, Heat conduction

© 2023 Marek Wojciechowski, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Palabras clave
Homogenization, Finite element method, Generalized boundary conditions, Darcy flow, Heat conduction