Article
Mathematics, Applied
Di Yang, Yinnian He, Luling Cao
Summary: In this study, a new analysis strategy is proposed to establish an a priori estimate of weak solutions to the steady-state dual-porosity Navier-Stokes fluid flow model with the Beavers-Joseph-Saffman interface condition. The a priori estimate and existence result are shown to be independent of small data and large viscosity restriction, with global uniqueness of the weak solution also proven.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
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
Yuxin Bi, Li Shan, Haicheng Zhang
Summary: This paper presents and analyzes a decoupled method for the nonstationary dual-porosity-Stokes coupling problem, dividing the problem into four subproblems to improve computational efficiency. Stability analysis and error estimation show that the scheme is stable and optimally convergent on a bounded time interval if the rescaling factor is small enough.
APPLIED NUMERICAL MATHEMATICS
(2022)
Article
Mathematics, Applied
Meilan Qiu, Fang Qing, Xijun Yu, Jiangyong Hou, Dewang Li, Xiaolong Zhao
Summary: This work presents a coupled finite element method to solve the stationary dual-porosity Navier-Stokes system with the Beavers-Joseph interface condition and the normal balance forces condition, without including the additional inertial term. The main mathematical challenge of this system is the indefinite leading order contributed by the Beavers-Joseph condition to the total energy. A proper re-scaling factor is introduced to overcome this difficulty and transform the original problem into a new space for analysis. The study establishes an a priori estimate, as well as the existence and local uniqueness, under suitable assumptions of physical parameters and sufficient fluid viscosity. Error estimates and convergence of the coupled finite element approximation are also obtained. Two numerical experiments are conducted to demonstrate the robustness of the proposed algorithm and the characteristics of the coupled system.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
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
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
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
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
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
Mathematics, Applied
Aycil Cesmelioglu, Sander Rhebergen
Summary: We present and analyze a strongly conservative hybridizable discontinuous Galerkin finite element method for the coupled incompressible Navier-Stokes and Darcy problem with Beavers-Joseph-Saffman interface condition. An a priori error analysis shows that the velocity error does not depend on the pressure, and that velocity and pressure converge with optimal rates. These results are confirmed by numerical examples.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mechanics
Essam Nabil Ahmed, Alessandro Bottaro
Summary: This study focuses on the fully developed, steady, incompressible, laminar flow in a channel with rough and/or permeable walls. The influence of micro-structured boundary surfaces on the flow behavior is simulated using high-order effective boundary conditions derived from homogenization theory without empirical parameters. A closed-form solution of the Navier-Stokes equations is obtained for the flow in the channel, incorporating slip velocities, shear stress, and streamwise pressure gradient at each virtual boundary. The accuracy and applicability of the model are validated against full feature-resolving simulations for different textures. The Stokes-based model used to identify slip and interface permeability coefficients in the effective boundary conditions is reliable and accurate up to a certain threshold, beyond which advective effects need to be considered.
EUROPEAN JOURNAL OF MECHANICS B-FLUIDS
(2024)
Article
Mathematics, Applied
Luling Cao, Yinnian He, Jian Li
Summary: This paper proposes and analyzes a parallel Robin-Robin domain decomposition method based on the modified characteristic finite element method for solving the time-dependent dual-porosity-Navier-Stokes model. The coupling terms are treated explicitly, taking advantage of previous time steps' information to construct a non-iterative domain decomposition method. Numerical examples demonstrate the effectiveness and efficiency of the proposed method.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
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
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
Zhongjie Lu, A. Cesmelioglu, J. J. W. Van der Vegt, Yan Xu
JOURNAL OF SCIENTIFIC COMPUTING
(2017)
Article
Mathematics, Applied
Aycil Cesmelioglu, Bernardo Cockburn, Weifeng Qiu
MATHEMATICS OF COMPUTATION
(2017)
Article
Mathematics, Applied
Aycil Cesmelioglu
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2017)
Article
Mathematics, Interdisciplinary Applications
A. Cesmelioglu, M. Song, D. Drignei
SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION
(2017)
Article
Mathematics, Applied
Susanne C. Brenner, Aycil Cesmelioglu, Jintao Cui, Li-Yeng Sung
COMPUTATIONAL METHODS IN APPLIED MATHEMATICS
(2018)
Article
Mathematics, Applied
Aycil Cesmelioglu, Bernardo Cockburn, Ngoc Cuong Nguyen, Jaume Peraire
JOURNAL OF SCIENTIFIC COMPUTING
(2013)
Article
Mathematics, Applied
Aycil Cesmelioglu, Prince Chidyagwai
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2020)
Article
Mathematics, Applied
Aycil Cesmelioglu, Sander Rhebergen, Garth N. Wells
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2020)
Article
Mathematics, Applied
Keegan L. A. Kirk, Aycil Cesmelioglu, Sander Rhebergen
Summary: This article proves the convergence of a space-time hybridized discontinuous Galerkin method for the evolutionary Navier-Stokes equations as the time step and mesh size approach zero, and further demonstrates that the weak solution satisfies the energy inequality. The analysis is carried out using discrete functional analysis tools and a discrete version of the Aubin-Lions-Simon theorem.
MATHEMATICS OF COMPUTATION
(2022)
Article
Mathematics, Applied
Aycil Cesmelioglu, Sander Rhebergen
Summary: We present and analyze a strongly conservative hybridizable discontinuous Galerkin finite element method for the coupled incompressible Navier-Stokes and Darcy problem with Beavers-Joseph-Saffman interface condition. An a priori error analysis shows that the velocity error does not depend on the pressure, and that velocity and pressure converge with optimal rates. These results are confirmed by numerical examples.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Aycil Cesmelioglu, Jeonghun J. Lee, Sander Rhebergen
Summary: We introduce and analyze a hybridizable discontinuous Galerkin finite element method for the coupled Stokes-Biot problem. The method has the property that the discrete velocities and displacements satisfy the compressibility equations pointwise on the elements. We prove well-posedness of the discretization and provide a priori error estimates that demonstrate the method is free of volumetric locking. Numerical examples further demonstrate optimal rates of convergence for all unknowns and locking-free discretization.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Aycil Cesmelioglu, Dinh Dong Pham, Sander Rhebergen
Summary: In this paper, a high-order hybridized discontinuous Galerkin (HDG) method is presented for the fully coupled time-dependent Stokes-Darcy-transport problem. The HDG method ensures compatibility between the discrete flow equations and the discrete transport equation. It also guarantees strong mass conservation and handles the interface conditions between the Stokes and Darcy regions effectively. A linearizing decoupling strategy is employed to sequentially solve the Stokes/Darcy and transport equations. Well-posedness and optimal a priori error estimates are proven for the velocity and concentration. Numerical examples demonstrate the compatibility and robustness of the discrete solution.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
(2023)
Article
Mathematics, Applied
Aycil Cesmelioglu, Sander Rhebergen
Summary: This study presents a stability and error analysis of an embedded-hybridized discontinuous Galerkin finite element method for coupled Stokes-Darcy flow and transport. The compatibility and stability of the coupled flow and transport discretization are demonstrated, along with the existence and uniqueness of the semi-discrete transport problem and optimal a priori error estimates. Numerical examples illustrate the theoretical results, showing that compatible discretization eliminates spurious oscillations in the solution to the transport problem caused by incompatible discretization.
COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
K. L. A. Kirk, T. L. Horvath, A. Cesmelioglu, S. Rhebergen
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2019)