Article
Computer Science, Interdisciplinary Applications
Jijie Lou, Jim E. Morel
Summary: This paper presents a High-Order/Low-Order radiation-hydrodynamics method that is second-order accurate in both space and time and uses the Variable Eddington Factor (VEF) method for coupling. Numerical calculations demonstrate the accuracy and asymptotic preserving properties of the method for smooth solutions and in the equilibrium-diffusion limit.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Engineering, Multidisciplinary
Wietse M. Boon, Dennis Glaeser, Rainer Helmig, Ivan Yotov
Summary: The flux-mortar mixed finite element method is developed for domain decomposition saddle point problems on non-matching grids. It uses the multipoint flux approximation as the subdomain discretization and solves positive definite cell-centered pressure systems. The mortar coupling variable is the normal flux on the subdomain interfaces and plays the role of a Lagrange multiplier for weakly continuous pressure. The method is reformulated as a mixed finite element method with a quadrature rule for well-posedness and error analysis. A non-overlapping domain decomposition algorithm and an efficient interface preconditioner are proposed for solving the resulting algebraic system.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Mustafa E. Danis, Jue Yan
Summary: This study proposes a new formula for the nonlinear viscous numerical flux and extends it to the compressible Navier-Stokes equations using the direct discontinuous Galerkin method with interface correction (DDGIC). The new method simplifies the implementation and enables accurate calculation of physical quantities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics
Zhendong Luo, Yuejie Li
Summary: The unsaturated flow problem is important and the mixed finite element method can be used to calculate water content and flux in soil. However, this method involves many unknowns. By using proper orthogonal decomposition, the dimension of the unknown solutions can be reduced, resulting in lighter workload, saved time, and improved accuracy in calculations.
Article
Mathematics, Applied
Eunjung Lee, Hyesun Na
Summary: The LL*-method is a least-squares finite element approach that solves a dual problem for approximation in partial differential equations. It has advantages for problems with low regularities and when L2-approximation is needed. However, piecewise polynomial approximation in LL* can generate artifacts such as spurious oscillations near shocks or discontinuities in the solution. This paper presents a stabilized LL*-method that aims to reduce these oscillations effectively. The consistency and error convergence of the proposed method are analyzed and numerical examinations are conducted.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
William Doherty, Timothy N. Phillips, Zhihua Xie
Summary: The implementation of a conservative level-set method in the mathematical framework of viscoelastic flow is the main original contribution of this paper. The finite element method is used to discretize the governing equations, and stabilisation of the constitutive equation is achieved using either the discontinuous Galerkin or streamline upwinding method. The discrete elastic viscous stress splitting gradient formulation is also employed in the Navier-Stokes equations. The numerical scheme is validated and shows excellent agreement with published data for both Newtonian and viscoelastic fluids in single and multiphase flows. The behavior of a gas bubble rising in a viscoelastic fluid is studied, considering the influence of polymer concentration, surface tension, fluid elasticity, and shear-thinning behavior on flow features.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Automation & Control Systems
Zhangqi Liu, K. Wang, Haiyang Sun, Jian Li, Bo Zhou
Summary: This article introduces a variable flux reluctance machine (VFRM) with dc field excitation and modular structure, which exhibits controllable flux, simplified manufacture, better fault tolerant capability, and potentially reduced material consumption. The operational theory is illustrated by using flux modulation principles and parameters are optimized by two-dimensional finite element method to maximize performance. The electromagnetic performance of nonmodular and modular VFRM is compared, including various characteristics and fault analysis.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
(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
Computer Science, Interdisciplinary Applications
Shuairun Zhu, Lulu Zhang, Lizhou Wu, Lin Tan, Haolong Chen
Summary: This paper investigates the effectiveness of the cascadic multigrid method applied to the improved Picard iteration method for solving nonlinear problems in deforming variably saturated porous media. Two improved Picard iteration methods are proposed, and their effectiveness is verified through numerical examples. The results show that the improved methods have faster convergence and higher computational efficiency compared to the classical method.
COMPUTERS AND GEOTECHNICS
(2024)
Article
Engineering, Civil
Yong Zhou, Bigya Gyawali, Weiping Zhang
Summary: This paper proposes a 3D pore network model to simulate the capillary absorption of water in unsaturated concrete. The model is developed using the Fuller particle distribution to generate aggregate particles and the principle of Laguerre tessellation to represent the equivalent capillary pores. The diffusion equation is solved on the interfaces between the polyhedron cells using the finite element method, considering the effect of gravity and changes in pore structure. The 3D pore network model accurately predicts the moisture content distribution within the concrete specimen over time.
Article
Physics, Multidisciplinary
Shucheng Huang, Junhui Yin, Li Xu, Bin Li
Summary: This study develops a flow solver based on the curvilinear DG method for solving three-dimensional subsonic, transonic, and hypersonic inviscid flows on unstructured meshes. The research demonstrates limitations of linear treatment on high-order flow accuracy and shows how boundary treatment involving curved elements can overcome these restrictions. The new techniques proposed in the study provide enhanced numerical simulations with low root mean square errors.
FRONTIERS IN PHYSICS
(2022)
Article
Multidisciplinary Sciences
Muhammad Shakhawat Hossain, Chunguang Xiong, Huafei Sun
Summary: In this research article, a discontinuous Galerkin method with weighted parameter theta and penalty parameter gamma is proposed for solving first order hyperbolic equations. The main objective of this method is to design error estimation for both a priori and a posteriori error analysis on general finite element meshes. The reliability and effectiveness of both parameters in the order of convergence of the solutions are also examined. A residual adaptive mesh-refining algorithm is employed for a posteriori error estimation. A series of numerical experiments are presented to illustrate the efficiency of the method.
Article
Mathematics
Denis Spiridonov, Maria Vasilyeva, Aleksei Tyrylgin, Eric T. Chung
Summary: This paper introduces a multiscale model reduction technique using an Online Generalized Multiscale finite element method for unsaturated filtration problem in fractured porous media. The method allows for high accuracy results with small computational costs through the use of offline and online multiscale basis functions.
Article
Computer Science, Interdisciplinary Applications
Anis Younes, Behshad Koohbor, Marwan Fahs, Hussein Hoteit
Summary: This work introduces a new model for simulating variable density flow in fractured porous media using advanced cell-centered numerical methods. The model utilizes a hybrid mixed finite element method for flow discretization in the matrix and fracture continua, and the discontinuous Galerkin method for advection-dominated transport in fractures. It ensures continuity of various properties at matrix-fracture interfaces and intersection of fractures. The model also uses high-order adaptive time integration techniques for time discretization, improving accuracy and efficiency.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Engineering, Multidisciplinary
Andrea La Spina, Jacob Fish
Summary: The work proposes a hybridizable discontinuous Galerkin (HDG) method for weakly compressible magnetohydrodynamic (MHD) problems, demonstrating its superior properties and superconvergence characteristics. Different MHD formulations are discussed, and the convergence properties of the proposed methods under various conditions are extensively examined through numerical examples.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Environmental Sciences
Anis Younes, Qian Shao, Thierry Alex Mara, Husam Musa Baalousha, Marwan Fahs
Article
Water Resources
Behshad Koohbor, Marwan Fahs, Hussein Hoteit, Joanna Doummar, Anis Younes, Benjamin Belfort
ADVANCES IN WATER RESOURCES
(2020)
Article
Environmental Sciences
Sabri Kanzari, Issam Daghari, Jiri Simunek, Anis Younes, Riadh Ilahy, Sana Ben Mariem, Mourad Rezig, Bechir Ben Nouna, Hassouna Bahrouni, Mohamed Ali Ben Abdallah
Article
Environmental Sciences
Guillaume Drouin, Marwan Fahs, Boris Droz, Anis Younes, Gwenael Imfeld, Sylvain Payraudeau
Summary: Pollutant exchange in the hyporheic zone is a major process controlling its degradation in river systems. The study combined laboratory tracer experiments and a flow reactive transport model to investigate mass exchange at the sediment-water interface (SWI). The experimental and numerical results showed good agreement, confirming the robustness of the model in capturing interactions between pollutant transport and partitioning in river sediment.
WATER RESOURCES RESEARCH
(2021)
Editorial Material
Environmental Sciences
Anis Younes, Marwan Fahs, Philippe Ackerer
Summary: Modeling fluid flow and transport processes in porous media is a challenging task due to the complex physical processes and mathematical models involved. Continual exploration of new methods and model parameters is necessary to enhance understanding in this field.
Article
Water Resources
Xiangjuan Yang, Qian Shao, Hussein Hoteit, Jesus Carrera, Anis Younes, Marwan Fahs
Summary: This study investigates three-dimensional natural convection processes in heterogeneous porous media using a meshless Fourier series approach. By considering a large-scale Rayleigh number to account for heterogeneity, it is found that the method is highly accurate for 3D natural convection problems.
ADVANCES IN WATER RESOURCES
(2021)
Article
Green & Sustainable Science & Technology
Paiman Shafabakhsh, Behzad Ataie-Ashtiani, Craig T. Simmons, Anis Younes, Marwan Fahs
Summary: Storing carbon dioxide in geological formations is effective in reducing greenhouse gas emissions. Fractures play a significant role in the migration and reactions of CO2, affecting storage capacity and plume growth. Neglecting fractures can impact the amount of trapped CO2, especially at low dissolution rates.
INTERNATIONAL JOURNAL OF GREENHOUSE GAS CONTROL
(2021)
Article
Water Resources
Anis Younes, Hussein Hoteit, Rainer Helmig, Marwan Fahs
Summary: The study developed a fully mixed finite element model for nonlinear flow and transport in unsaturated fractured porous media by spatial discretization of 2D matrix elements and 1D fracture elements and using efficient time discretization methods, addressing challenges such as infiltration of contaminated water into dry soil.
ADVANCES IN WATER RESOURCES
(2022)
Article
Environmental Sciences
Francois Lehmann, Mohammad Mahdi Rajabi, Benjamin Belfort, Frederick Delay, Marwan Fahs, Philippe Ackerer, Anis Younes
Summary: This study proposes a novel experimental setup for reconstructing multiple fracture limestone media using glass beads and parallelepiped-shaped limestone beams. Three models of transport through fractured media are investigated under different flow conditions, and the results show that only the NLMIM model is able to accurately capture the experimental results.
JOURNAL OF CONTAMINANT HYDROLOGY
(2022)
Article
Computer Science, Interdisciplinary Applications
Anis Younes, Behshad Koohbor, Marwan Fahs, Hussein Hoteit
Summary: This work introduces a new model for simulating variable density flow in fractured porous media using advanced cell-centered numerical methods. The model utilizes a hybrid mixed finite element method for flow discretization in the matrix and fracture continua, and the discontinuous Galerkin method for advection-dominated transport in fractures. It ensures continuity of various properties at matrix-fracture interfaces and intersection of fractures. The model also uses high-order adaptive time integration techniques for time discretization, improving accuracy and efficiency.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Water Resources
Sara Tabrizinejadas, Anis Younes, Hussein Hoteit, Jerome Carrayrou, Marwan Fahs
Summary: Modeling dissolution processes in discrete fracture networks (DFNs) is a challenging task. In this work, an advanced Discontinuous Galerkin (DG) model is developed to simulate transport with dissolution in DFNs. The model successfully captures the nonlinear coupling between flow, mass transport, and reactive processes associated with fracture aperture evolution by dissolution. Numerical examples show that the DG-DFN model avoids unphysical oscillations and reduces numerical diffusion, providing accurate and efficient simulations of flow, transport, and aperture evolution processes in DFNs.
ADVANCES IN WATER RESOURCES
(2023)
Article
Computer Science, Interdisciplinary Applications
Lingai Guo, Marwan Fahs, Behshad Koohbor, Hussein Hoteit, Anis Younes, Rui Gao, Qian Shao
Summary: The main goal of this paper is to extend the application of the MHFEM to HM processes in fractured domains by combining it with XFEM. The new scheme (MHFEM-XFEM) significantly reduces the computational burden and provides high accuracy compared to the standard finite element method.
COMPUTERS AND GEOTECHNICS
(2023)
Article
Water Resources
Husam Musa Baalousha, Anis Younes, Mohamed A. Yassin, Marwan Fahs
Summary: Flood risk assessment is an important tool for urban planning, land development, and hydrological analysis, especially in arid countries where the flood risks are high. This study used GIS and the Fuzzy Analytic Hierarchy Process (F-AHP) to assess the flood risk in Qatar based on factors such as land cover, soil type, precipitation, elevation, and flow accumulation, as well as the exposure impact of land use. The results showed that the majority of urbanized areas in Qatar are within the high-risk zone, indicating the accuracy and effectiveness of the F-AHP method.
Article
Geosciences, Multidisciplinary
Anis Younes, Hussein Hoteit, Rainer Helmig, Marwan Fahs
Summary: The mixed finite element method is suitable for simulating fluid flow in heterogeneous porous media, but it can generate unphysical oscillations when used for the transport equation. This work proposes a robust upwind MFE scheme that combines the upwind finite volume method with the hybrid formulation of the MFE method. Numerical simulations show that the new scheme generates stable solutions without oscillations and is robust for solving nonlinear problems.
HYDROLOGY AND EARTH SYSTEM SCIENCES
(2022)