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This study proposes a new discrete neural operator for surrogate modeling of transient Darcy flow fields in heterogeneous porous media with random parameters. The new method integrates temporal encoding, operator learning and UNet to…

Numerical Analysis · Mathematics 2025-12-04 Zhenglong Chen , Zhao Zhang , Xia Yan , Jiayu Zhai , Piyang Liu , Kai Zhang

As a typical multiphase fluid flow process, drainage in porous media is of fundamental interest in nature and industrial applications. During drainage processes in unsaturated soils and porous media in general, saturated clusters, in which…

Soft Condensed Matter · Physics 2018-02-22 Shuoqi Li , Mingchao Liu , Dorian Hanaor , Yixiang Gan

This paper explores the application of the multiscale finite element method (MsFEM) to address steady-state Stokes-Darcy problems with BJS interface conditions in highly heterogeneous porous media. We assume the existence of multiscale…

Numerical Analysis · Mathematics 2024-01-09 Yachen Hong , Wenhan Zhang , Lina Zhao , Haibiao Zheng

In this paper, we consider the flow of an incompressible fluid in a deformable porous solid. We present a mathematical model using the framework offered by the theory of interacting continua. In its most general form, this framework…

Numerical Analysis · Computer Science 2013-02-27 D. Z. Turner , K. B. Nakshatrala , M. J. Martinez

Macroporous silicon is widely employed in sensing and optoelectronic applications due to its large internal surface area and adjustable pore structure. However, quantitative correlations between morphology and functionality require…

Materials Science · Physics 2026-04-09 A. Ramírez-Porras , I. Prado , N. R. Schwarz , U. Steiner

The estimation of the permeability of porous media to fluids is of fundamental importance in fields as diverse as oil and gas industry, agriculture, hydrology and medicine. Despite more than 150 years since the publication of Darcy's linear…

Fluid Dynamics · Physics 2024-06-07 Tairone Paiva Leão

The paper develops an unfitted finite element method for solving the Darcy system of equations posed in a network of fractures embedded in a porous matrix. The approach builds on the Hughes--Masud stabilized formulation of the Darcy problem…

Numerical Analysis · Mathematics 2019-09-04 Alexey Y. Chernyshenko , Maxim A. Olshanskii

This review examined the current advancements in data-driven methods for analyzing flow and transport in porous media, which has various applications in energy, chemical engineering, environmental science, and beyond. Although there has…

Fluid Dynamics · Physics 2024-07-01 Guang Yang , Ran Xu , Yusong Tian , Songyuan Guo , Jingyi Wu , Xu Chu

We use novel, fast 4D Synchrotron X-ray imaging with large field-of-view to reveal pore- and macro-scale drainage dynamics during gas-brine flow through a layered sandstone rock sample. We show that a single centimetre-scale layer, similar…

Fluid Dynamics · Physics 2025-11-10 Catrin Harris , Sam Krevor , Ann H Muggeridge , Michael Camilleri , Samuel J. Jackson

We consider a Darcy problem for saturated porous media written in dual formulation in presence of a fully immersed inclusion. The lowest order virtual element method is employ to derive the discrete approximation. In the present work we…

Numerical Analysis · Mathematics 2019-08-01 Alessio Fumagalli

In this paper we examine how porosity fluctuations affect the hydrodynamic permeability of a porous matrix or membrane. We introduce a fluctuating Darcy model, which couples the Navier-Stokes equation to the space- and time-dependent…

Soft Condensed Matter · Physics 2026-02-25 Albert Dombret , Adrien Sutter , Baptiste Coquinot , Nikita Kavokine , Benoit Coasne , Lydéric Bocquet

Quantitative structure-property relationships are crucial for the understanding and prediction of the physical properties of complex materials. For fluid flow in porous materials, characterizing the geometry of the pore microstructure…

Soft Condensed Matter · Physics 2020-09-21 Magnus Röding , Zheng Ma , Salvatore Torquato

Porous materials are ubiquitous in various engineering and geological applications, where their permeability plays a critical role in viscous fluid flow and transport phenomena. Understanding and characterizing the microscale properties,…

Fluid Dynamics · Physics 2025-03-11 David Krach , Matthias Ruf , Holger Steeb

Two-phase surfactant-laden flow and transport in porous media are central to many natural and engineering applications. Surfactants alter two-phase flow by modifying interfacial tension and wettability, while two-phase flow controls…

Fluid Dynamics · Physics 2026-02-02 Sidian Chen , Bo Guo , Tianyuan Zheng

Flow interaction between a plain-fluid region in contact with a porous layer attracted significant attention from modelling and analysis sides due to numerous applications in biology, environment and industry. In the most widely used…

Numerical Analysis · Mathematics 2025-09-03 Linheng Ruan , Iryna Rybak

We propose an approach that links density functional theory (DFT) and molecular dynamics (MD) simulation to study fluid behavior in nanopores in contact with bulk (macropores). It consists of two principal steps. First, the theoretical…

Computational Physics · Physics 2021-07-06 Mariia Vaganova , Irina Nesterova , Yuriy Kanygin , Andrey Kazennov , Aleksey Khlyupin

Systems comprising a turbulent channel flow overlaying a permeable bed can be found in a variety of industrial and natural applications (e.g. urban planning, fracking, submerged vegetation). One important realization of this system is at…

Fluid Dynamics · Physics 2017-08-01 Benjamin H. Sonin

In this paper, a pore-scale network modeling method, based on the flow continuity residual in conjunction with a Newton-Raphson non-linear iterative solving technique, is proposed and used to obtain the pressure and flow fields in a network…

Fluid Dynamics · Physics 2014-12-02 Taha Sochi

Superhydrophobic surfaces with multi-scale topographies offer exceptionally high apparent water contact angles and low contact angle hysteresis by virtue of the small liquid{\textendash}solid contact fractions they enable. Natural…

Applied Physics · Physics 2019-12-16 Soochan Chung , Kristyn Kadala , Hayden Taylor

Among the different contributions generating self-potential, the streaming potential is of particular interest in hydrogeology for its sensitivity to water flow. Estimating water flux in porous media using streaming potential data relies on…

Geophysics · Physics 2019-05-01 Luis Guarracino , Damien Jougnot