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
Pierre-Henri Cocquet, Michael Rakotobe, Delphine Ramalingom, Alain Bastide
Summary: This paper deals with the finite element approximation of the Darcy-Brinkman-Forchheimer equation for porous media with spatially-varying porosity and mixed boundary conditions. It proves uniqueness of the solution under certain conditions and convergence of the finite element approximation. Numerical experiments are provided to illustrate the theoretical results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Review
Chemistry, Multidisciplinary
Hossam A. Nabwey, Taher Armaghani, Behzad Azizimehr, Ahmed M. Rashad, Ali J. Chamkha
Summary: This paper presents a review of recent advances in the application of nanofluids in heat transfer in porous materials. The top papers published between 2018 and 2020 were scrutinized to provide valuable insights. Various analytical methods used to describe flow and heat transfer in porous media were thoroughly reviewed, as well as the models used to simulate nanofluids. The reviewed research focused on natural convection, forced convection, and mixed convection heat transfer of nanofluids in porous media. Statistical analysis revealed important findings regarding the impact of parameters such as nanofluid type and flow domain geometry. Furthermore, the paper highlighted the most commonly studied nanofluid and geometry.
Article
Energy & Fuels
Abadelhalim Elsanoose, Ekhwaiter Abobaker, Faisal Khan, Mohammad Azizur Rahman, Amer Aborig, Stephen D. Butt
Summary: This study conducted a radial flow experiment to investigate the existence of non-Darcy flow and calculate the non-Darcy inertia coefficient. The experiments were performed on seven cylindrical perforated artificial porous media samples, and it was found that the non-Darcy flow exists even at very low flow rates. Additionally, the study revealed that the non-Darcy effect is not only caused by turbulence but also by inertial effects.
Article
Water Resources
Xinyu Wu, Hui Guo, Ziyao Xu, Yang Yang
Summary: We propose a novel hybrid-dimensional model for the Darcy-Forchheimer flow in fractured rigid porous media, with a natural applicability to non-conforming meshes. The model couples the Darcy's law in the matrix and the Forchheimer's law in the fractures by introducing Dirac functions to characterize the fractures. The model has been validated through numerical experiments and shows effectiveness on non-conforming meshes.
ADVANCES IN WATER RESOURCES
(2023)
Article
Mathematics, Applied
Isabelle Gruais, Dan Polisevski
Summary: This study examines the thermal flow problem in fractured porous medium, involving incompressible filtration flow in porous matrix and viscous flow in fractures, with coupling through Saffman's variant of Beavers-Joseph condition. Existence and uniqueness properties are discussed, showing the appropriateness of using energy norm to describe Darcy-Forchheimer law. In the epsilon-periodic framework, a two-scale homogenized system governing their behavior in the limit where the Forchheimer effect vanishes is found, mainly modeling two coupled thermal flows.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
(2021)
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
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
Energy & Fuels
Yuanqing Wu, Jisheng Kou, Shuyu Sun
Summary: This paper investigates the numerical simulation of matrix acidization in fractured porous media. By combining the continuum fracture model and the DarcyBrinkman-Forchheimer framework, accurate results can be obtained using a simple simulation framework. The findings of this study have practical implications for real operations.
JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING
(2022)
Article
Thermodynamics
B. Shruti, Md. Mahbub Alam, A. Parkash, S. Dhinakaran
Summary: In this study, the combined impact of Darcy and Rayleigh number changes on natural convection around two vertically arranged hot porous cylinders of different diameters in a square enclosure is numerically evaluated. The numerical simulations are conducted using the lattice Boltzmann technique and the D2Q9 model. It is found that heat transfer rates improve with an increase in cylinder size, Ra, and Da.
CASE STUDIES IN THERMAL ENGINEERING
(2023)
Article
Energy & Fuels
Xue-Yi Zhang, Zhi Dou, Jin-Guo Wang, Zhi-Fang Zhou, Chao Zhuang
Summary: Compared to single layer porous media, fluid flow through layered porous media with contrasting pore space structures is more complex. This study constructed three-dimensional pore-scale layered porous media and analyzed the influence of interfaces on non-Darcy flow behavior. The results indicate that existing correlations based on single layer porous media fail to accurately predict the flow behavior of layered porous media.
Article
Multidisciplinary Sciences
Jose Luis Diaz Palencia, Saeed Ur Rahman, Antonio Naranjo Redondo, Julian Roa Gonzalez
Summary: The goal of this study is to provide analytical and numerical assessments for fluid flow in a porous media using an Eyring-Powell viscosity term and a Darcy-Forchheimer law. The analysis explores regularity, existence, and uniqueness of solutions, and utilizes the Geometric Perturbation Theory to study travelling wave solutions near equation critical points. Additionally, a numerical routine is provided to validate the analytical approach for low Reynolds numbers in a porous medium.
Article
Engineering, Multidisciplinary
Quan M. Bui, Francois P. Hamon, Nicola Castelletto, Daniel Osei-Kuffuor, Randolph R. Settgast, Joshua A. White
Summary: Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and design efficient and safe operations, numerical simulations are widely used. Fully-implicit time-stepping schemes are often necessary to avoid time-step stability restrictions, but face challenges with the computational bottleneck of linear solvers. A flexible strategy based on multigrid reduction (MGR) is proposed to handle these challenges and demonstrate efficiency and scalability through numerical examples.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Chemical
Alessandro Lenci, Farhad Zeighami, Vittorio Di Federico
Summary: This study focuses on inertial flow in porous media governed by the Forchheimer equation and its relation to domain heterogeneity at the field scale. It proposes a method to derive formulae for the effective Forchheimer coefficient in perfectly stratified media. The effective Forchheimer coefficient varies with flow direction and is influenced by factors such as heterogeneity, exponent c, and permeability distribution.
TRANSPORT IN POROUS MEDIA
(2022)
Article
Materials Science, Multidisciplinary
Fabian B. Wadsworth, Jeremie Vasseur, Michael J. Heap, Lucille Carbillet, Donald B. Dingwell, Thierry Reuschle, Patrick Baud
Summary: Sintered materials are widely used in various applications, but a validated and general model of porosity and permeability is crucial. In this study, we prepare samples of different glass bead populations sintered at high temperature and measure their porosity and permeability. By combining our new dataset with published data, we find that a percolation theory model shows good agreement and requires no empirical adjustment. However, we propose some semi-empirical steps to generalize this model across all porosities. Additionally, we investigate the inertial component of fluid transport at high flow rates through these materials.
Article
Mathematics, Applied
A. Arraras, L. Portero
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2019)
Article
Mathematics, Applied
Carmen Rodrigo, Francisco J. Gaspar, Ludmil T. Zikatanov
JOURNAL OF COMPUTATIONAL MATHEMATICS
(2019)
Article
Mathematics, Applied
Manuel Borregales, Kundan Kumar, Florin Adrian Radu, Carmen Rodrigo, Francisco Jose Gaspar
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2019)
Article
Mathematics, Applied
A. Pe de la Riva, F. J. Gaspar, C. Rodrigo
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2020)
Article
Computer Science, Interdisciplinary Applications
Andres Arraras, Francisco J. Gaspar, Laura Portero, Carmen Rodrigo
Summary: The proposed efficient blackbox-type multigrid method solves multipoint flux approximations of the Darcy problem on logically rectangular grids by combining interpolation, restriction operators, and relaxation procedures, demonstrating robust convergence for different coefficient problems and rough quadrilateral grids.
COMPUTATIONAL GEOSCIENCES
(2021)
Proceedings Paper
Education & Educational Research
E. Romero, E. Perez, C. Rodrigo
14TH INTERNATIONAL TECHNOLOGY, EDUCATION AND DEVELOPMENT CONFERENCE (INTED2020)
(2020)
Article
Mathematics, Applied
J. H. Adler, F. J. Gaspar, X. Hu, P. Ohm, C. Rodrigo, L. T. Zikatanov
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2020)
Proceedings Paper
Computer Science, Theory & Methods
Francisco J. Gaspar, Carmen Rodrigo, Xiaozhe Hu, Peter Ohm, James Adler, Ludmil Zikatanov
NUMERICAL METHODS AND APPLICATIONS, NMA 2018
(2019)
Article
Mathematics, Applied
Andres Arraras, Francisco J. Gaspar, Laura Portero, Carmen Rodrigo
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2019)
Article
Mathematics, Applied
Junfeng Cao, Ke Chen, Huan Han
Summary: This paper proposes a two-stage image segmentation model based on structure tensor and fractional-order regularization. In the first stage, fractional-order regularization is used to approximate the Hausdorff measure of the MS model. The solution is found using the ADI scheme. In the second stage, thresholding is used for target segmentation. The proposed model demonstrates superior performance compared to state-of-the-art methods.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Dylan J. Oliver, Ian W. Turner, Elliot J. Carr
Summary: This paper discusses a projection-based framework for numerical computation of advection-diffusion-reaction (ADR) equations in heterogeneous media with multiple layers or complex geometric structures. By obtaining approximate solutions on a coarse grid and reconstructing solutions on a fine grid, the computational cost is significantly reduced while accurately approximating complex solutions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Nathan V. Roberts, Sean T. Miller, Stephen D. Bond, Eric C. Cyr
Summary: In this study, the time-marching discontinuous Petrov-Galerkin (DPG) method is applied to the Vlasov equation for the first time, using backward Euler for a Vlasov-Poisson discretization. Adaptive mesh refinement is demonstrated on two problems: the two-stream instability problem and a cold diode problem.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Yizhi Sun, Zhilin Sun
Summary: This work investigates the convexity of a specific class of positive definite probability measures and demonstrates the preservation of convexity under multiplication and intertwining product. The study reveals that any integrable function on an interval with a polynomial expansion of fast absolute convergence can be decomposed into a pair of positive convex interval probabilities, simplifying the study of interval distributions and discontinuous probabilistic Galerkin schemes.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Bhagwan Singh, Komal Jangid, Santwana Mukhopadhyay
Summary: This paper examines the prediction of bending characteristics of nanoscale materials using the Moore-Gibson-Thompson thermoelasticity theory in conjunction with the nonlocal strain gradient theory. The study finds that the stiffness of the materials can be affected by nonlocal and length-scale parameters, and the aspect ratios of the beam structure play a significant role in bending simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Guoliang Wang, Bo Zheng, Yueqiang Shang
Summary: This paper presents and analyzes a parallel finite element post-processing algorithm for the simulation of Stokes equations with a nonlinear damping term, which integrates the algorithmic advantages of the two-level approach, the partition of unity method, and the post-processing technique. The algorithm generates a global continuous approximate solution using the partition of unity method and improves the smoothness of the solution by adding an extra coarse grid correction step. It has good parallel performance and is validated through theoretical error estimates and numerical test examples.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Hao Xu, Zeng-Qi Wang
Summary: Fluid flow control problems are crucial in industrial applications, and solving the optimal control of Navier-Stokes equations is challenging. By using Oseen's approximation and matrix splitting preconditioners, we can efficiently solve the linear systems and improve convergence.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhengya Yang, Xuejuan Chen, Yanping Chen, Jing Wang
Summary: This paper focuses on the high-order stable numerical solutions of the time-space fractional diffusion equation. The Fourier spectral method is used for spatial discretization and the Spectral Deferred Correction (SDC) method is used for numerical solutions in time. As a result, a high-precision numerical discretization scheme for solving the fractional diffusion equation is obtained, and the convergence and stability of the scheme are proved. Several numerical examples are presented to demonstrate the effectiveness and feasibility of the proposed numerical scheme.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)