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A method of computational homogenization of a heterogeneous porous medium based on a hyperbolic thermodynamically compatible model Научная публикация

Журнал

Journal of Computational and Applied Mathematics
ISSN: 0377-0427

Вых. Данные

Год: 2027, Том: 491, Номер статьи : 118064, Страниц : 21 DOI: 10.1016/j.cam.2026.118064

Ключевые слова

Effective elastic moduli, Heterogeneous saturated porous medium, Strain energy-based method, Time marching method for steady-state solution, Diffuse interface, Hyperbolic thermodynamically compatible model

Авторы

Romenski Evgeniy ¹ , Reshetova Galina ²

Организации

1	Sobolev Institute of Mathematics SB RAS
2	Trofimuk Institute of Petroleum Geology and Geophysics SB RAS

Информация о финансировании (1)

Министерство науки и высшего образования РФ

075-15-2025-348

A method for evaluating effective elastic moduli of fluid-saturated deformable porous materials is proposed. The approach is based on calculating the strain energy of a heterogeneous medium and comparing it with the energy of an equivalent homogeneous elastic medium. Heterogeneity is described using a Hyperbolic Thermodynamically Compatible (HTC) system of equations for a porous medium, simplified for small deformations; this formulation permits the use of a diffuse interface representation in the presence of regions occupied by either purely elastic solid or pure fluid. By comparing the energies of the porous medium and its equivalent elastic counterpart while solving a series of simple stationary stress-strain problems for a sample, all components of the effective compliance tensor, and consequently all components of the effective stiffness tensor, together with the corresponding effective wave velocities can be determined. For the numerical solution of the governing equations, a high-order finite difference scheme on a staggered grid is applied. To obtain stationary equilibrium solutions for the sample, a steady state is reached via a time-marching technique incorporating artificial velocity relaxation. A series of test problems demonstrate the flexibility of the method when applied to various types of saturated porous samples. Comparisons are made with known theoretical predictions of effective moduli for selected media. In particular, it is shown that for a liquid-saturated porous elastic sample with a simple periodic microstructure, the elastic moduli employed in the HTC model are accurately approximated by the numerically obtained effective moduli.

Romenski E. , Reshetova G.
A method of computational homogenization of a heterogeneous porous medium based on a hyperbolic thermodynamically compatible model
Journal of Computational and Applied Mathematics. 2027. V.491. 118064 :1-21. DOI: 10.1016/j.cam.2026.118064 WOS Scopus OpenAlex

Поступила в редакцию:	10 мар. 2026 г.
Принята к публикации:	29 июл. 2026 г.
Опубликована online:	11 авг. 2026 г.

≡ Web of science:	WOS:001851358500001
≡ Scopus:	2-s2.0-105047322752
≡ OpenAlex:	W7202188774