Article
Mathematics, Applied
Y. I. N. I. N. G. Cao, X. I. A. O. M. I. N. G. Wang
Summary: This study proves that the difference between the solutions to the Stokes-Darcy system derived using the Beavers-Joseph or Beavers-Joseph-Saffman-Jones interfacial conditions is proportional to the Darcy number when the Reynolds number is below a certain threshold. Therefore, the Beavers-Joseph-Saffman-Jones interface boundary condition is an excellent approximation of the classical Beavers-Joseph interface boundary condition in the regime of small Darcy numbers.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Yingzhi Liu, Yinnian He, Xuejian Li, Xiaoming He
Summary: This paper demonstrates the convergence analysis of the Robin-Robin domain decomposition method for the Stokes-Darcy system with Beavers-Joseph interface condition, focusing on the case of convergence for small viscosity and hydraulic conductivity. Utilizing discrete techniques, the almost optimal geometric convergence rate for gamma(f) > gamma(p) is obtained. The results provide a general guideline for choosing parameters to achieve convergence and geometric convergence rate, which is confirmed by numerical simulations.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Luling Cao, Yinnian He, Jian Li, Di Yang
Summary: This paper develops the numerical theory of decoupled modified characteristic FEMs for the fully evolutionary Navier-Stokes-Darcy model with the Beavers-Joseph interface condition. The optimal L-2-norm error convergence order of the solutions is proved by mathematical induction, implying the uniform L-2-boundedness of the fully discrete velocity solution. High efficiency of this method is demonstrated through numerical tests.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Zhipeng Yang, Ju Ming, Changxin Qiu, Maojun Li, Xiaoming He
Summary: A multigrid multilevel Monte Carlo (MGMLMC) method is developed for the stochastic Stokes-Darcy interface model with random hydraulic conductivity. The method aims to efficiently solve the stochastic model, especially focusing on the interface and the random Beavers-Joseph interface condition.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
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
Xinhui Wang, Guangzhi Du, Yi Li
Summary: In this paper, a modified local and parallel finite element method (MLPFEM) is proposed for the coupled Stokes-Darcy problem. The method combines a partition of unity with backtracking technique to improve computational efficiency while maintaining global continuity, and achieves optimal error bounds.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Guangzhi Du, Shilin Mi, Xinhui Wang
Summary: This paper provides and studies some local and parallel finite element methods based on two-grid discretizations for the non-stationary Stokes-Darcy model with the Beavers-Joseph interface condition. Two local algorithms, the semi-discrete and fully discrete finite element algorithms, are introduced and related error estimates are derived. Two fully discrete parallel algorithms are subsequently developed based on the fully discrete local algorithm. The validity of the algorithms is illustrated through numerical results.
NUMERICAL ALGORITHMS
(2023)
Article
Thermodynamics
Malik Zaka Ullah, Taseer Muhammad, Fouad Mallawi
Summary: This paper theoretically studies the 3D nanofluid flow with zero nanoparticles mass and constant heat fluxes conditions. A bidirectional stretchable sheet is used to produce the three-dimensional flow, and appropriate variables are considered to transform the PDEs into ODEs. The results show the impact of emerging flow factors on concentration and temperature of nanoparticles, as well as the relationship between heat transport rate and skin frictions.
JOURNAL OF THERMAL ANALYSIS AND CALORIMETRY
(2021)
Article
Mathematics, Applied
Feng Shi, Yizhong Sun, Haibiao Zheng
Summary: In this paper, an efficient ensemble domain decomposition algorithm is proposed for fast solving the fully mixed random Stokes--Darcy model with the physically realistic Beavers-Joseph interface conditions. The algorithm utilizes the Monte Carlo method to derive deterministic numerical models for the coupled model with random inputs, and uses the idea of ensemble to realize fast computation of multiple problems. The algorithm achieves comparable accuracy with traditional methods by sharing a common coefficient matrix in each deterministic numerical model, significantly reducing computational cost.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2023)
Article
Thermodynamics
J. C. Umavathi, Bernardo Buonomo, Oronzio Manca, Mikhail A. Sheremet
Summary: This study investigates mixed convection of permeable fluid in a vertical channel with Robin conditions, considering the effects of chemical reactions. Solutions are obtained using numerical schemes, revealing the significant influence of the thermal Grashof number and Brinkman number on flow rate and concentration patterns.
THERMAL SCIENCE AND ENGINEERING PROGRESS
(2021)
Article
Engineering, Multidisciplinary
Sifat Hussain, Zaheer Abbas, Jafar Hasnain, M. Shakib Arslan, Amjad Ali
Summary: This paper presents a parametric study for the flow characteristic and heat transmission of MHD TiO2-water nanofluid in a permeable channel with expanding or contracting walls with thermal radiation. Various mathematical methods are used to solve non-linear ordinary differential equations, and it is found that slip and magnetic parameters influence velocity and friction, while radiation parameter affects temperature profile and Nusselt number.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
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
Denis Spiridonov, Maria Vasilyeva
Summary: This research presents the application of the non-local multicontinuum method (NLMC) to describe the Darcy-Forchheimer model in fractured media. The mathematical model can describe the nonlinear flow with high inertial effect and flow speed. The embedded fracture model (EFM) is used to approximate lower dimensional fractures, while the finite volume method (FVM) is employed for spatial approximation on a fine grid. Furthermore, a non-local model reduction approach is proposed based on localization and constraint energy minimization, and multiscale basis functions are constructed in oversampled local domains to consider the flow effects from neighboring local domains. The numerical results demonstrate that the non-local multicontinuum method can provide highly accurate results for Darcy-Forchheimer flow in fractured media.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Engineering, Chemical
Paula Strohbeck, Elissa Eggenweiler, Iryna Rybak
Summary: Physically consistent coupling conditions and effective parameters are crucial for accurate modeling and simulation of various applications at the fluid-porous interface. The commonly used Beavers-Joseph condition for tangential velocity is only suitable for parallel flows and its slip coefficient value is uncertain.
TRANSPORT IN POROUS MEDIA
(2023)
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)
