Article
Mathematics, Applied
Sima Mashayekhi, Seyed Nourollah Mousavi
Summary: In this study, European options are numerically solved using the finite difference method and Monte Carlo simulation with variance reduction technique. Results show that the proposed method with grid stretching transformation and antithetic variate method outperforms other schemes in terms of accuracy.
Article
Mathematics, Applied
Amit Kumar Verma, Mukesh Kumar Rawani, Carlo Cattani
Summary: This paper introduces a numerical method based on Haar wavelet collocation method and a nonstandard finite difference scheme for solving a class of generalized Burgers' equation. The method is easy to implement, efficient, and produces results in great agreement with analytical solutions for a small number of grid points.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics
S. Gheraibia, A. Guesmia
Summary: This paper investigates the stability of a solar pond by studying the effect of the entrainment velocity, Nusselt number, and thickness of the salinity gradient zone. The study uses numerical methods to establish a relationship between the salinity gradient and temperature gradient in the gradient zone. The results highlight an additional condition for the stability of solar ponds.
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
(2021)
Article
Mathematics, Applied
Shujuan Lu, Tao Xu, Zhaosheng Feng
Summary: In this study, a second-order finite difference scheme is proposed for analyzing a class of space-time variable-order fractional diffusion equation. The scheme is demonstrated to be unconditionally stable and convergent with a convergence order of O(tau(2) + h(2)) under certain conditions, as validated by numerical examples.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Geosciences, Multidisciplinary
Wei Liu, Ziduo Hu, Xueshan Yong, Gengxin Peng, Zhonghua Xu, Linghe Han
Summary: This paper proposes a new mixed staggered-grid finite-difference scheme (M-SFD) to improve the modeling accuracy and stability. By constructing the spatial FD operator to approximate the first-order spatial partial derivative, M-SFD achieves higher modeling accuracy and computational efficiency compared to the conventional scheme. The application of M-SFD in reverse time migration effectively eliminates imaging artifacts caused by numerical dispersion and improves imaging accuracy and resolution.
FRONTIERS IN EARTH SCIENCE
(2022)
Article
Computer Science, Theory & Methods
S. Zabihi, R. Ezzati, F. Fattahzadeh, J. Rashidinia
Summary: Our study introduces, discusses, and investigates approximate solutions to the fuzzy Wave equation on a finite domain utilizing generalized Hukuhara partial differentiability. A computationally effective algorithm based on the fuzzy finite difference is proposed. According to the results, the method gives an accurate solution to the fuzzy Wave equation.
FUZZY SETS AND SYSTEMS
(2023)
Article
Mathematics, Applied
Xindong Zhang, Lin Yao, Juan Liu
Summary: The article proposes a two-level mesh method for solving the nonlinear Fisher's equation, using global radial basis function method and radial basis function-finite difference method on coarse and fine meshes respectively. The numerical results demonstrate the method is highly effective.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Environmental Sciences
Shihao Wang, Xiangyu Yu, Philip H. Winterfeld, Yu-Shu Wu
Summary: In this paper, an efficient and reasonably accurate program called FracCSM is presented for the numerical modeling of dynamic fractures in hydraulic fracturing operations. FracCSM combines the Integrated Finite Difference (IFD) method and Discontinuous Displacement Method (DDM) to simulate the initiation, propagation, and stress interference effects of hydraulic fractures. It also considers mass/heat transport inside fractures and frictional losses within the wellbore. FracCSM demonstrates sound accuracy in comparison with existing simulators and supports real-time simulation of fracture propagation.
Article
Energy & Fuels
Dominik Blonski, Katarzyna Strzelecka, Henryk Kudela
Summary: This paper presents a numerical implementation of a penalized vortex in cell method for solving airfoil flow problems with a focus on the vortex trapping cavity. Analysis of different airfoil shapes and angles was conducted to assess the impact of vortex trapping cavities on aerodynamic performance.
Article
Mathematics, Applied
Wenxiang Sun, Haodong Ma, Wenzhen Qu
Summary: This paper introduces a hybrid numerical technique, combining the KDC method and the GFDM method, for solving two-dimensional nonlinear transient heat conduction problems with temperature-dependent thermal conductivity. The accuracy and stability of the method are verified through two numerical experiments, demonstrating its strong performance for simulating the interested problems in long-time intervals.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Chenxi Wang, Alina Chertock, Shumo Cui, Alexander Kurganov, Zhen Zhang
Summary: In this paper, a coupled chemotaxis-fluid system is studied to model the self-organized collective behavior of oxytactic bacteria in a sessile drop. A new positivity preserving and high-resolution method based on the diffuse-domain approach is developed to solve the chemotaxis-fluid system. Numerical experiments are performed to demonstrate the performance of the proposed approach on different shapes of sessile drops, showing interesting chemotactic phenomena.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
F. Herrero-Hervas, M. Negreanu, A. M. Vargas
Summary: This article studies a parabolic-elliptic system that models the pattern formation in E. coli bacteria in response to a chemoattractant. It considers bacterial strains with motility regulation and uses the Generalized Finite Difference Method for numerical solution. The article explains the derivation of the explicit formulae, studies the convergence of the explicit scheme, and provides examples over regular and irregular meshes.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Computer Science, Interdisciplinary Applications
Mahboubeh Tavakoli Tameh, Fatemeh Shakeri
Summary: We propose a robust and effective method for solving the biharmonic interface problem with discontinuities in both the solution and its derivatives. This method decouples the biharmonic equation into two Poisson equations and combines the method of difference potentials with finite difference schemes on regular structured grid to achieve high-order accuracy on nonconforming domains. Representative numerical experiments confirm the accuracy, effectiveness, and ability of the proposed method to handle problems with coupled equations.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2022)
Article
Mathematical & Computational Biology
Lin Zhang, Yongbin Ge, Xiaojia Yang
Summary: The Keller-Segel model is a crucial tool for simulating biological processes, consisting of a reaction-diffusion-chemotaxis equation and a reaction-diffusion equation. However, most numerical methods used to solve this model lack accuracy in the temporal direction. Therefore, a high-precision and stable compact difference scheme is proposed in this study, which employs a fourth-order backward difference formula and compact difference operators for discretization. The proposed method is verified through numerical experiments, including finite-time blow-up, non-negativity, mass conservation, and energy dissipation.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Article
Mathematics
Binxin Yang, Zhifeng Wang, Zhijuan Meng
Summary: The existing phase field model of polymer crystallization contains parameters that lack actual physical meaning. A new phase field model is proposed in this paper, which can simulate various forms of polymer crystals by adjusting the latent heat. The simulation results are consistent with experimental data and provide a theoretical basis for the preparation and optimization of high-performance polymers.
Article
Engineering, Environmental
Wei Shen, Tonglu Li, Ping Li, Yueqiang Shen, Yulu Lei, Jian Guo
BULLETIN OF ENGINEERING GEOLOGY AND THE ENVIRONMENT
(2019)
Article
Engineering, Geological
Ping Li, Wei Shen, Xiaokun Hou, Tonglu Li
ENGINEERING GEOLOGY
(2019)
Article
Engineering, Geological
Wei Shen, Tonglu Li, Ping Li, Matteo Berti, Yueciiang Shen, Jian Guo
ENGINEERING GEOLOGY
(2019)
Article
Engineering, Geological
Jian Guo, Shujian Yi, Yanzhou Yin, Yifei Cui, Mingyue Qin, Tonglu Li, Chenyang Wang
Article
Engineering, Geological
Yan Yan, Yifei Cui, Xin Tian, Sheng Hu, Jian Guo, Ziang Wang, Shuyao Yin, Liufeng Liao
Article
Engineering, Geological
Dingzhu Liu, Yifei Cui, Jian Guo, Zhilin Yu, Dave Chan, Mingyu Lei
Article
Engineering, Geological
Xinghua Zhu, Jianbing Peng, Bangxiao Liu, Cheng Jiang, Jian Guo
ENGINEERING GEOLOGY
(2020)
Article
Engineering, Geological
Yan Yan, Yifei Cui, Jian Guo, Sheng Hu, Ziang Wang, Shuyao Yin
ENGINEERING GEOLOGY
(2020)
Article
Environmental Sciences
Wei Shin, Tong-lu Li, Matteo Berti, Ping Li, Yu-lu Lei, Yue-qiang Shen
Summary: An improved model was proposed to study the influence of bed deposition phenomenon in flow-like landslides. The results showed that bed deposition dissipates part of the kinetic energy of the landslide, while reducing friction energy dissipation, contributing to its high mobility.
JOURNAL OF MOUNTAIN SCIENCE
(2021)
Article
Engineering, Geological
Jian Guo, Jiao Wang, Yao Li, Shujian Yi
Summary: The landslide-induced debris flow in Wangcang County, Sichuan Province on August 14, 2020, resulted in three deaths and two destroyed houses. Factors such as continuous rainfall, interbedded marlstone with structural planes, and changes in slope gradient contributed to the disaster. The study findings may serve as a reference for future research on geohazard chains.
Article
Environmental Sciences
Yao Li, Peng Cui, Chengming Ye, Jose Marcato Junior, Zhengtao Zhang, Jian Guo, Jonathan Li
Summary: This study introduces a deep learning framework that considers the source area feature of earthquake-induced landslides (EQIL) for spatial prediction. By using high-resolution remote sensing images and DEM to extract EQIL source areas and utilizing a stacked autoencoder for feature extraction, the model outperforms traditional methods in accuracy and effectively identifies the spatial distribution of EQIL.
Article
Engineering, Geological
Jian Guo, Yifei Cui, Wenjie Xu, Yanzhou Yin, Yao Li, Wen Jin
Summary: This study used the discrete element method to analyze the dynamic processes of a debris flow event in Dujiangyan city, China. The results showed two different scenarios of rock slide and bed entrainment, as well as the transformation of landslide to debris flow during short-term blockage.
Article
Geosciences, Multidisciplinary
Yao Shunyu, Nazir Ahmed Bazai, Tang Jinbo, Jiang Hu, Yi Shujian, Zou Qiang, Tashfain Ahmed, Guo Jian
Summary: This study analyzed the impact of topography on the movement process of a debris flow in Wujia Gully, China. The debris flow was found to be a typical viscous debris flow with four stages in its dynamic process, and the topography played a significant role in the formation of these stages. Additionally, Manning's resistance coefficient affected the velocity and duration of each stage.
Article
Engineering, Geological
Mingyue Qin, Peng Cui, Yao Jiang, Jian Guo, Guotao Zhang, Muhammad Ramzan
Summary: Vegetation is an important factor in controlling shallow landslides in vegetation-covered areas. However, existing infiltration process models often neglect or simplify the root system, making it difficult to capture the influence of root systems on shallow landslides. This study quantitatively investigated the root distribution and properties in a landslide-prone area in Yunnan Province, China. The results showed that the root distribution followed an exponential decay model and there were differences in physical and hydraulic properties between soil above and below the slip surface. The findings suggest that root distribution and resulting changes in soil properties can affect slope stability and induce shallow landslides.
Article
Geography, Physical
Yan Yan, Yifei Cui, Xinghui Huang, Jiaojiao Zhou, Wengang Zhang, Shuyao Yin, Jian Guo, Sheng Hu
Summary: This study developed a method combining seismic signal inversion and numerical simulation to provide comprehensive and accurate dynamic process reconstruction of the 2018 Baige landslide in China. The study found that the landslide was triggered by detachment of the weathered layer, with severe top fault segmentation, and comprised initiation, main slip, blocking, and deposition stages. Mutual verification of multiple methods effectively reduced inherent drawbacks and improved the rationality and reliability of the results.
EARTH SURFACE DYNAMICS
(2022)
