Article
Mathematics, Applied
Rui Li, Yongchao Zhang, Jianhua Wu, Zhangxin Chen
Summary: This paper presents a numerical simulation of the single phase Darcy flow model in two-dimensional fractured porous media. The model is described as a reduced problem by coupling the bulk problem in porous matrix and the fracture problem in fractures. Numerical experiments demonstrate the accuracy, flexibility, and robustness of the discrete formulation for complicated networks of fractures in porous media domain.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Chemistry, Multidisciplinary
Feng Xiong, Yijun Jiang, Chun Zhu, Lin Teng, Hao Cheng, Yajun Wang
Summary: This study focuses on the nonlinear flow in fractured porous media. The finite volume method is used to derive the discrete equations for Darcy flow in porous media and Forchheimer flow in fractures. A solution method for coupling flow is proposed. The results show that the hydraulic gradient of surrounding rock is characterized by large at the bottom and small at the top. The flow rate at the bottom of the tunnel is greater than that at the top. The distribution homogeneity and density of fractures are the most important factors that affect the hydraulic behavior of fractured rock tunnels.
APPLIED SCIENCES-BASEL
(2023)
Article
Mathematics, Applied
Manal Alotaibi, Huangxin Chen, Shuyu Sun
Summary: In this work, the generalized multiscale finite element method (GMsFEM) is combined with a reduced model based on the discrete fracture model (DFM) to efficiently and accurately simulate flow in fractured porous media. The GMsFEM represents fracture effects on a coarse grid using multiscale basis functions constructed from local spectral problems. The proposed reduction technique, which considers permeability in both fracture and matrix domain, has significant impact on solving large and complex systems resulting from modeling flow in fractured porous media.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Zhengkang He, Huangxin Chen, Jie Chen, Zhangxin Chen
Summary: The paper introduces a multiscale method for solving Darcy flow in two-dimensional fractured porous media, using appropriate elements and integration rules to obtain mass matrices with specific features for easy velocity elimination and reduced computational complexity.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Applied
Lina Zhao, Dohyun Kim, Eun-Jae Park, Eric Chung
Summary: In this paper, a staggered discontinuous Galerkin method for Darcy flows in fractured porous media is presented and analyzed. The method uses a staggered discontinuous Galerkin method and a standard conforming finite element method with appropriate inclusion of interface conditions. The optimal convergence estimates for all the variables are proved, and the error estimates are shown to be fully robust with respect to the heterogeneity and anisotropy of the permeability coefficients.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Computer Science, Interdisciplinary Applications
Sara Shokrollahzadeh Behbahani, Hadi Hajibeygi, Denis Voskov, Jan Dirk Jansen
Summary: A smoothed embedded finite-volume modeling method is proposed for faulted and fractured heterogeneous poroelastic media. This method achieves coupling between fault slip mechanics, deformation mechanics, and fluid flow equations to ensure stability and consistency of simulation results. The method also addresses the challenge of oscillatory stress fields at faults through a smoothed embedded strategy. The sEFVM provides locally conservative mass flux and stress fields on a staggered grid, showing promise for field-scale relevant simulation of induced seismicity.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Zahra Mehrdoost
Summary: The multiscale finite volume method is developed for discrete fracture modeling in highly heterogeneous porous media, with efficient algorithms devised for generating adaptive unstructured coarse grids. Significant improvement of the method in highly heterogeneous fractured porous media is achieved, with good accuracy in flow simulation in challenging test cases.
ENGINEERING WITH COMPUTERS
(2021)
Article
Computer Science, Interdisciplinary Applications
Fanxiang Xu, Hadi Hajibeygi, Lambertus J. Sluys
Summary: The multiscale XFEM proposed in this work addresses the challenges of complex multiscale geoscientific applications by utilizing locally computed enriched basis functions. Through algebraic formulation and solving methods, this approach significantly reduces computational costs while maintaining accuracy, making it a promising scalable method for large-scale heavily fractured porous media.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics
Dossan Baigereyev, Nurlana Alimbekova, Abdumauvlen Berdyshev, Muratkan Madiyarov
Summary: This paper focuses on the construction and analysis of numerical methods for solving a differential equation describing fluid flow in fractured porous media, with a main emphasis on demonstrating the convergence of the numerical schemes and validating their practical applications.
Article
Computer Science, Interdisciplinary Applications
Wei Liu, Yanping Chen, Zhifeng Wang, Jian Huang
Summary: This paper investigates the coupling of a slightly compressible Darcy-Brinkman-transport problem in fractured media with higher Reynolds numbers. It introduces a new two-layer reduced coupled model that treats the fracture as a hyperplane. The finite difference method is used to solve the new model on staggered nonuniform grids, and the uniqueness, existence, and convergence rate of the numerical method are derived. Experimental results demonstrate the accuracy and efficiency of the method, and numerical analysis showcases the behavior of fluid flow and solute transport in different types of fractures in the media.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Dennis Glaeser, Martin Schneider, Bernd Flemisch, Rainer Helmig
Summary: This study compared different numerical schemes for simulating flow in fractured porous media, including two new vertex-centered approaches and established methods. The new schemes showed less degrees of freedom on unstructured simplex grids and produced results in good agreement with established methods.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Geosciences, Multidisciplinary
Tao Huang, Xin Liao, Zhaoqin Huang, Renyi Wang
Summary: Ferrofluid, a magnetic fluid, has attracted extensive attention in the oil industry due to its controllable flow by an external magnetic field. Studies have shown that the flow of ferrofluid in complex porous media is significantly affected by magnetic force, offering potential for enhancing oil recovery efficiency in oil fields.
FRONTIERS IN EARTH SCIENCE
(2021)
Article
Environmental Sciences
G. D. Beskardes, C. J. Weiss, K. L. Kuhlman, K. W. Chang
Summary: In this study, the hierarchical finite element method (Hi-FEM) is used to simulate fluid flow and heat conduction in complex geological environments. The method incorporates hierarchical basis functions and the Yeh's Galerkin model to accurately model fractured porous media, demonstrating its reliability in large-scale simulations with complex fracture networks.
WATER RESOURCES RESEARCH
(2022)
Article
Water Resources
D. Hernandez, E. C. Herrera-Hernandez
Summary: This study presents different Generalized Double Porosity Models for anomalous fluid flow in fractured porous media and discusses their applications in transient production decline. It explores the effects of subdiffusive and superdiffusive flows in fracture networks, coupled with subdiffusive transport inside the matrix, and provides insights into identifying these types of flow in geological formations. Additionally, it discusses different interpretations of model parameters for estimating the length scales of system main heterogeneities and shows that superdiffusive flow regimes could result from highly heterogeneous porous systems with scale-free permeability distributions. Finally, it demonstrates that the use of non-local models discussed here allows for a novel way to construct effective single porosity models for describing double porosity systems over the long term.
ADVANCES IN WATER RESOURCES
(2021)
Article
Mathematics, Applied
Loubna Salhi, Mofdi El-Amrani, Mohammed Seaid
Summary: This paper investigates the performance of a unified finite element method for the numerical solution of moving fronts in porous media under non-isothermal flow conditions. The governing equations consist of coupling the Darcy equation for the pressure to two convection-diffusion-reaction equations for the temperature and depth of conversion. A non-oscillatory unified Galerkin-characteristic method is developed for efficient simulation of moving fronts in porous media by combining the modified method of characteristics with a Galerkin finite element discretization of the governing equations. The proposed method uses the same finite element space for all solutions to the problem including the pressure, velocity, temperature, and concentration. Analysis of convergence and stability is presented, and error estimates in the L-2-norm are established for the numerical solutions. The method is verified for the benchmark problem of moving fronts around an array of cylinders, and the numerical results obtained demonstrate its ability to capture the main flow features.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Philippe Angot, Gilles Carbou, Victor Peron
ASYMPTOTIC ANALYSIS
(2016)
Article
Mathematics
Philippe Angot, Jean-Paul Caltagirone, Pierre Fabrie
COMPTES RENDUS MATHEMATIQUE
(2016)
Article
Mathematics, Applied
Philippe Angot, Rima Cheaytou
MATHEMATICS OF COMPUTATION
(2018)
Article
Mathematics, Applied
Philippe Angot
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
(2018)
Article
Mathematics, Applied
Philippe Angot, Jean-Paul Caltagirone, Pierre Fabrie
APPLIED MATHEMATICS LETTERS
(2013)
Article
Computer Science, Interdisciplinary Applications
Philippe Angot, Thomas Auphan, Olivier Gues
JOURNAL OF COMPUTATIONAL PHYSICS
(2014)
Article
Physics, Mathematical
Philippe Angot, Rima Cheaytou
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2019)
Article
Chemistry, Applied
R. Hernandez-Rodriguez, B. Goyeau, P. Angot, J. A. Ochoa-Tapia
REVISTA MEXICANA DE INGENIERIA QUIMICA
(2020)
Article
Water Resources
Philippe Angot, Benoit Goyeau, J. Alberto Ochoa-Tapia
Summary: The derived model for inertial fluid flow through a fluid-porous interface is nonlinear and multi-dimensional, suitable for arbitrary flow directions. The model considers a thin transition porous layer between the pure fluid and homogeneous porous region, with nonlinear momentum jump conditions at the equivalent dividing interface. This innovative asymptotic model opens new perspectives for studying turbulent flows at fluid-porous interfaces.
ADVANCES IN WATER RESOURCES
(2021)
Article
Mathematics, Applied
Mohamed Kara, Salim Mesbahi, Philippe Angot
Summary: This study focuses on the jump-integrated boundary conditions method in the context of fictitious domain methods for the elasticity problem, using a proposed finite volume method for the vector elasticity system. The approach was numerically validated for various test cases, serving as a preliminary step before tackling more challenging fluid-structure interactions or moving interface problems.
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
(2021)
Article
Mathematics, Applied
Philippe Angot, Zhilin Li
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
(2017)
Article
Physics, Fluids & Plasmas
Philippe Angot, Benoit Goyeau, J. Alberto Ochoa-Tapia
Proceedings Paper
Mathematics, Applied
Thomas Auphan, Philippe Angot, Olivier Gues
HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS
(2014)
Proceedings Paper
Mathematics
Philippe Angot, Thomas Auphan, Olivier Gues
FINITE VOLUMES FOR COMPLEX APPLICATIONS VII - ELLIPTIC, PARABOLIC AND HYPERBOLIC PROBLEMS, FVCA 7
(2014)
Proceedings Paper
Computer Science, Interdisciplinary Applications
Philippe Angot, Rima Cheaytou