Article
Mathematics, Applied
Zhen Guan, Xiaodong Wang, Jie Ouyang
Summary: In this paper, an improved finite difference/finite element method is proposed for the fractional Rayleigh-Stokes problem with a nonlinear source term. The method utilizes a linearized difference scheme along with the second-order backward differentiation formula and weighted Grunwald-Letnikov difference formula for time discretization, achieving higher stability and convergence accuracy than previous works. Numerical examples are also provided to validate the theoretical results.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2021)
Article
Mathematics, Applied
Liming Guo, Wenbin Chen
Summary: In this paper, a decoupled stabilized finite element method is proposed for solving the time-dependent Navier-Stokes/Biot problem. The coupling problem is divided into two subproblems and solved using different numerical methods. The stability analysis and error estimates are provided to validate the effectiveness of the proposed method.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Computer Science, Interdisciplinary Applications
Farzaneh Safari, HongGuang Sun
Summary: The improved singular boundary method (ISBM) and dual reciprocity method (DRM) are coupled to solve the Rayleigh-Stokes problem with a fractional derivative and nonhomogeneous term. The method is simple, stable, and proven to be accurate and efficient through numerical results.
ENGINEERING WITH COMPUTERS
(2021)
Article
Physics, Mathematical
Hui Yao, Mejdi Azaiez, Chuanju Xu
Summary: This paper proposes efficient schemes for the Navier-Stokes equations, utilizing the Uzawa algorithm and modified algorithms to overcome existing shortcomings. Energy stability and error analysis are conducted for first- and second-order schemes, and simulations demonstrate the robustness and efficiency of the proposed schemes at high Reynolds numbers.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Marziyeh Saffarian, Akbar Mohebbi
Summary: In this paper, we investigated the Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivatives, which plays a crucial role in describing the dynamic behavior of non-Newtonian fluids. We proposed a high order numerical method to solve the two-dimensional case of this equation on regular and irregular regions, and demonstrated its accuracy and efficiency through numerical simulations.
ENGINEERING WITH COMPUTERS
(2023)
Article
Mathematics, Applied
Ian Kesler, Rihui Lan, Pengtao Sun
Summary: In this paper, a nonconservative arbitrary Lagrangian-Eulerian (ALE) finite element method is developed for a transient Stokes/parabolic moving interface problem with jump coefficients. The stability and optimal convergence properties of both semi- and full discretizations are analyzed in terms of the energy norm, demonstrating its effectiveness for fluid-structure interaction (FSI) problems.
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
(2021)
Article
Engineering, Multidisciplinary
Zakieh Avazzadeh, Omid Nikan, Anh Tuan Nguyen, Van Tien Nguyen
Summary: This paper presents an efficient stabilized meshless technique with a hybrid kernel to simulate the fractional Rayleigh-Stokes problem for an edge in a viscoelastic fluid. The proposed method approximates the unknown solution through two phases: temporal discretization and space discretization. The localized approach considers neighboring collocation nodes to avoid ill-conditioning in matrix systems, and the convergence and stability properties are discussed theoretically and confirmed numerically.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Mathematics, Applied
Liming Guo, Wenbin Chen
Summary: The article proposes a decoupled modified characteristic finite element method for solving the time-dependent Navier-Stokes/Biot problem. The method uses implicit backward Euler scheme for time discretization and treats coupling terms explicitly. The stability and error estimates of the fully discrete scheme are established and validated through numerical experiments.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Robert Nuernberg
Summary: In this paper, a fully discrete approximation for solidification and liquidation of materials with negligible specific heat is introduced and analyzed. The model is a two-sided Mullins-Sekerka problem. The discretization uses finite elements in space and an independent parameterization of the moving free boundary. Unconditional stability and exact volume conservation are proven for the introduced scheme. Several numerical simulations, including simulations for nearly crystalline surface energies, demonstrate the practicality and accuracy of the presented numerical method.
JOURNAL OF NUMERICAL MATHEMATICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Tongxin Wang, Ziwen Jiang, Ailing Zhu, Zhe Yin
Summary: This paper studies the transverse vibration of a fractional viscoelastic beam using fractional calculus and the mixed finite volume element method. The stability and convergence of the algorithm are analyzed. Numerical examples demonstrate the effectiveness of the algorithm, and the test results show the significant effects of the damping coefficient and the fractional derivative on the model.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Hui Peng, Qilong Zhai, Ran Zhang, Shangyou Zhang
Summary: This paper proposes a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition, and validates the theoretical analysis through numerical experiments.
SCIENCE CHINA-MATHEMATICS
(2021)
Article
Mathematics, Applied
Omer Oruc
Summary: This paper presents an efficient numerical method for solving the two-dimensional fractional Rayleigh-Stokes problem for a heated generalized second grade fluid. The method is proven to be accurate and workable through numerical simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Mathematics, Applied
Liang Gao, Jian Li
Summary: In this paper, the decoupled stabilized finite element method for the dual-porosity-Navier-Stokes model is considered, which couples the free flow region and the microfracture-matrix system using four interface conditions. The method is decoupled in two levels, dividing the coupling problem into three subproblems in a non-iterative manner to improve computational efficiency. The stability and convergence of the decoupling scheme are also analyzed, and theoretical results are illustrated through numerical experiments.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Thomas Frachon, Sara Zahedi
Summary: This article proposes a new unfitted finite element method for simulating two-phase flows with insoluble surfactant. The method features discrete conservation of surfactant mass, the possibility of using non-conforming meshes, and accurate approximation of quantities across evolving geometries. The method combines a space-time cut finite element formulation with quadrature in time and a stabilization term for function extension. Numerical simulations in different dimensions are presented, including the interaction between two drops.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Qingfang Liu, Baotong Li, Yujie Wang, Zhiheng Wang, Jiakun Zhao
Summary: This paper presents a fully discrete two-grid mixed finite element scheme for simulating two immiscible and incompressible flows using a phase field model. The two-grid method is used to overcome computational difficulties caused by the strong nonlinear coupling system. The stability and convergence of the method are analyzed under certain assumptions, and numerical experiments are conducted to validate the theoretical analysis.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Engineering, Multidisciplinary
Mostafa Abbaszadeh, Ali Ebrahimijahan, Mehdi Dehghan
Summary: This article presents a numerical technique based on the compact local integrated radial basis function (CLI-RBF) method for solving ill-posed inverse heat problems (IHP) with continuous/discontinuous heat source. The space derivative is discretized using the CLIRBF procedure, resulting in a system of ODEs related to the time variable. The final system of ODEs is solved using an adaptive fourth-order Runge-Kutta algorithm. The new numerical method is verified through challenging examples and found to be accurate for solving IHP with continuous/discontinuous heat source in one-and two-dimensional cases.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Mathematics, Applied
Mostafa Abbaszadeh, Mohammad Ivan Azis, Mehdi Dehghan, Reza Mohammadi-Arani
Summary: This paper proposes a new meshless numerical procedure, namely the gradient smoothing method (GSM), for simulating the pollutant transition equation in urban street canyons. The time derivative is approximated using the finite difference scheme, while the space derivative is discretized using the gradient smoothing method. Additionally, the proper orthogonal decomposition (POD) approach is employed to reduce CPU time. Several real-world examples are solved to verify the efficiency of the developed numerical procedure.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Biology
Niusha Narimani, Mehdi Dehghan
Summary: This paper numerically studies the therapies of prostate cancer in a two-dimensional space. The proposed model describes the tumor growth driven by a nutrient and the effects of cytotoxic chemotherapy and antiangiogenic therapy. The results obtained without using any adaptive algorithm show the response of the prostate tumor growth to different therapies.
COMPUTERS IN BIOLOGY AND MEDICINE
(2023)
Article
Engineering, Multidisciplinary
Mostafa Abbaszadeh, Yasmin Kalhor, Mehdi Dehghan, Marco Donatelli
Summary: The purpose of this research is to develop a numerical method for option pricing in jump-diffusion models. The proposed model consists of a backward partial integro-differential equation with diffusion and advection factors. Pseudo-spectral technique and cubic B-spline functions are used to solve the equation, and a second-order Strong Stability Preserved Runge-Kutta procedure is adopted. The efficiency and accuracy of the proposed method are demonstrated through various test cases.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Mahboubeh Najafi, Mehdi Dehghan
Summary: In this work, two-dimensional dendritic solidification is simulated using the meshless Diffuse Approximate Method (DAM). The Stefan problem is studied through the phase-field model, considering both isotropic and anisotropic materials for comparisons. The effects of changing some constants on the obtained patterns are investigated.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Computer Science, Interdisciplinary Applications
Hasan Zamani-Gharaghoshi, Mehdi Dehghan, Mostafa Abbaszadeh
Summary: This paper presents a local meshless collocation method for solving reaction-diffusion systems on surfaces. The proposed numerical procedure utilizes Pascal polynomial approximation and closest point method. This method is geometrically flexible and can be used to solve partial differential equations on unstructured point clouds. It only requires a set of arbitrarily scattered mesh-free points representing the underlying surface.
ENGINEERING WITH COMPUTERS
(2023)
Article
Computer Science, Interdisciplinary Applications
Reza MohammadiArani, Mehdi Dehghan, Mostafa Abbaszadeh
Summary: Different coupled systems for the shallow water equation, bed elevation, and suspended load equation have been proposed. The main goal of this paper is to utilize an advanced lattice Boltzmann method (LBM) to solve this system of equations. In addition, a practical approach is developed for applying open boundary conditions in order to relax the solution onto a prescribed equilibrium flow.
ENGINEERING WITH COMPUTERS
(2023)
Article
Mathematics, Applied
Mehdi Dehghan, Zeinab Gharibi
Summary: This paper discusses the incompressible miscible displacement of two-dimensional Darcy-Forchheimer flow and formulates a mathematical model with two partial differential equations: a Darcy-Forchheimer flow equation for the pressure and a convection-diffusion equation for the concentration. The model is discretized using a fully mixed virtual element method (VEM) and stability, existence, and uniqueness of the associated mixed VEM solution are proved under smallness data assumption. Optimal error estimates are obtained for concentration, auxiliary flux variables, and velocity, and several numerical experiments are presented to support the theoretical analysis and illustrate the applicability for solving actual problems.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2023)
Article
Mathematics, Applied
Fatemeh Asadi-Mehregan, Pouria Assari, Mehdi Dehghan
Summary: In this research, we present a numerical approach for solving a specific type of nonlinear integro-differential equations derived from Volterra's population model. This model captures the growth of a biological species in a closed system and includes an integral term to account for toxin accumulation. The proposed technique utilizes the discrete Galerkin scheme with the moving least squares (MLS) algorithm to estimate the solution of the integro-differential equations.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2023)
Article
Mathematics, Applied
Mehdi Dehghan, Zeinab Gharibi, Ricardo Ruiz-Baier
Summary: In this article, a fully coupled, nonlinear, and energy-stable virtual element method (VEM) is proposed and analyzed for solving the coupled Poisson-Nernst-Planck (PNP) and Navier-Stokes (NS) equations. The stability, existence, and uniqueness of solution of the associated VEM are proved, and optimal error estimates for both the electrostatic potential and ionic concentrations of PNP equations, as well as for the velocity and pressure of NS equations, are derived. Numerical experiments are presented to support the theoretical analysis and demonstrate the method's performance in simulating electrokinetic instabilities in ionic fluids and studying their dependence on ion concentration and applied voltage.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Engineering, Multidisciplinary
Mostafa Abbaszadeh, AliReza Bagheri Salec, Alaa Salim Jebur
Summary: This paper investigates a time fractional distributed-order diffusion equation and analyzes its stability, convergence, and numerical accuracy.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Computer Science, Artificial Intelligence
Fatemeh Gholami, Zahed Rahmati, Alireza Mofidi, Mostafa Abbaszadeh
Summary: This research investigates and elaborates on graph machine learning methods applied to non-English datasets for text classification tasks. By utilizing different graph neural network architectures and ensemble learning methods, along with language-specific pre-trained models, the study shows improved accuracy in capturing the topological information between textual data, leading to better text classification performance.
Article
Mathematics, Applied
Reza MohammadiArani, Mehdi Dehghan, Mostafa Abbaszadeh
Summary: Lattice Boltzmann method is a powerful solver for fluid flow, but it is challenging to use it to solve other partial differential equations. This paper challenges the LBM to solve the two-dimensional DKS equation by finding a suitable local equilibrium distribution function and proposes a modification for implementing boundary conditions in complex geometries.
APPLIED NUMERICAL MATHEMATICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Mostafa Abbaszadeh, AliReza Bagheri Salec, Shurooq Kamel Abd Al-Khafaji
Summary: This paper proposes a numerical method using spectral collocation and POD approach to solve systems of space fractional PDEs. The method achieves high accuracy and computational efficiency.
ENGINEERING COMPUTATIONS
(2023)
