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High-Order Bound-Preserving Finite Difference Methods for Multispecies and Multireaction Detonations 被引量:1
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作者 Jie Du Yang Yang 《Communications on Applied Mathematics and Computation》 2023年第1期31-63,共33页
In this paper,we apply high-order finite difference(FD)schemes for multispecies and multireaction detonations(MMD).In MMD,the density and pressure are positive and the mass fraction of the ith species in the chemical ... In this paper,we apply high-order finite difference(FD)schemes for multispecies and multireaction detonations(MMD).In MMD,the density and pressure are positive and the mass fraction of the ith species in the chemical reaction,say zi,is between 0 and 1,withΣz_(i)=1.Due to the lack of maximum-principle,most of the previous bound-preserving technique cannot be applied directly.To preserve those bounds,we will use the positivity-preserving technique to all the zi'is and enforceΣz_(i)=1 by constructing conservative schemes,thanks to conservative time integrations and consistent numerical fluxes in the system.Moreover,detonation is an extreme singular mode of flame propagation in premixed gas,and the model contains a significant stiff source.It is well known that for hyperbolic equations with stiff source,the transition points in the numerical approximations near the shocks may trigger spurious shock speed,leading to wrong shock position.Intuitively,the high-order weighted essentially non-oscillatory(WENO)scheme,which can suppress oscillations near the discontinuities,would be a good choice for spatial discretization.However,with the nonlinear weights,the numerical fluxes are no longer“consistent”,leading to nonconservative numerical schemes and the bound-preserving technique does not work.Numerical experiments demonstrate that,without further numerical techniques such as subcell resolutions,the conservative FD method with linear weights can yield better numerical approximations than the nonconservative WENO scheme. 展开更多
关键词 Weighted essentially non-oscillatory scheme finite difference method Stiff source DETONATIONS Bound-preserving CONSERVATIVE
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Solution of a One-Dimension Heat Equation Using Higher-Order Finite Difference Methods and Their Stability
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作者 M. Emran Ali Wahida Zaman Loskor +1 位作者 Samia Taher Farjana Bilkis 《Journal of Applied Mathematics and Physics》 2022年第3期877-886,共10页
One-dimensional heat equation was solved for different higher-order finite difference schemes, namely, forward time and fourth-order centered space explicit method, backward time and fourth-order centered space implic... One-dimensional heat equation was solved for different higher-order finite difference schemes, namely, forward time and fourth-order centered space explicit method, backward time and fourth-order centered space implicit method, and fourth-order implicit Crank-Nicolson finite difference method. Higher-order schemes have complexity in computing values at the neighboring points to the boundaries. It is required there a specification of the values of field variables at some points exterior to the domain. The complexity was incorporated using Hicks approximation. The convergence and stability analysis was also computed for those higher-order finite difference explicit and implicit methods in case of solving a one dimensional heat equation. The obtained numerical results were compared with exact solutions. It is found that backward time and fourth-order centered space implicit scheme along with Hicks approximation performed well over the other mentioned higher-order approaches. 展开更多
关键词 Heat Equation Boundary Condition Higher-Order finite difference methods Hicks Approximation
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Finite Difference Methods for the Time Fractional Advection-diffusion Equation
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作者 MA Yan MUSBAH FS 《Chinese Quarterly Journal of Mathematics》 2019年第3期259-273,共15页
In this paper, three implicit finite difference methods are developed to solve one dimensional time fractional advection-diffusion equation. The fractional derivative is treated by applying right shifted Grünwald... In this paper, three implicit finite difference methods are developed to solve one dimensional time fractional advection-diffusion equation. The fractional derivative is treated by applying right shifted Grünwald-Letnikov formula of order α ∈(0, 1). We investigate the stability analysis by using von Neumann method with mathematical induction and prove that these three proposed methods are unconditionally stable. Numerical results are presented to demonstrate the effectiveness of the schemes mentioned in this paper. 展开更多
关键词 Time fractional advection-difusion finite difference method Griinwald-Letnikov formula STABILITY EFFECTIVENESS
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ONE-PARAMETER FINITE DIFFERENCE METHODS AND THEIR ACCELERATED SCHEMES FOR SPACE-FRACTIONAL SINE-GORDON EQUATIONS WITH DISTRIBUTED DELAY
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作者 Tao Sun Chengjian Zhang Haiwei Sun 《Journal of Computational Mathematics》 SCIE CSCD 2024年第3期705-734,共30页
This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed delay.For 1D problems,... This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed delay.For 1D problems,we construct a kind of oneparameter finite difference(OPFD)method.It is shown that,under a suitable condition,the proposed method is convergent with second order accuracy both in time and space.In implementation,the preconditioned conjugate gradient(PCG)method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD method.For 2D problems,we develop another kind of OPFD method.For such a method,two classes of accelerated schemes are suggested,one is alternative direction implicit(ADI)scheme and the other is ADI-PCG scheme.In particular,we prove that ADI scheme can arrive at second-order accuracy in time and space.With some numerical experiments,the computational effectiveness and accuracy of the methods are further verified.Moreover,for the suggested methods,a numerical comparison in computational efficiency is presented. 展开更多
关键词 Fractional sine-Gordon equation with distributed delay One-parameter finite difference methods Convergence analysis ADI scheme PCG method
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Analysis of Extended Fisher-Kolmogorov Equation in 2D Utilizing the Generalized Finite Difference Method with Supplementary Nodes
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作者 Bingrui Ju Wenxiang Sun +1 位作者 Wenzhen Qu Yan Gu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第10期267-280,共14页
In this study,we propose an efficient numerical framework to attain the solution of the extended Fisher-Kolmogorov(EFK)problem.The temporal derivative in the EFK equation is approximated by utilizing the Crank-Nicolso... In this study,we propose an efficient numerical framework to attain the solution of the extended Fisher-Kolmogorov(EFK)problem.The temporal derivative in the EFK equation is approximated by utilizing the Crank-Nicolson scheme.Following temporal discretization,the generalized finite difference method(GFDM)with supplementary nodes is utilized to address the nonlinear boundary value problems at each time node.These supplementary nodes are distributed along the boundary to match the number of boundary nodes.By incorporating supplementary nodes,the resulting nonlinear algebraic equations can effectively satisfy the governing equation and boundary conditions of the EFK equation.To demonstrate the efficacy of our approach,we present three numerical examples showcasing its performance in solving this nonlinear problem. 展开更多
关键词 Generalized finite difference method nonlinear extended Fisher-Kolmogorov equation Crank-Nicolson scheme
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Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems
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作者 Chunlei Ruan Cengceng Dong +2 位作者 Zeyue Zhang Boyu Chen Zhijun Liu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第9期2707-2728,共22页
Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using t... Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions. 展开更多
关键词 Peridynamic differential operator finite difference method STABILITY transient heat conduction problem
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ON BOUNDARY TREATMENT FOR THE NUMERICAL SOLUTION OF THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FINITE DIFFERENCE METHODS 被引量:1
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《Journal of Computational Mathematics》 SCIE CSCD 1996年第2期135-142,共8页
关键词 MATH ON BOUNDARY TREATMENT FOR THE NUMERICAL SOLUTION OF THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS WITH finite difference methods
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ON THE FINITE DIFFERENCE METHODS FOR TWO DIMENSIONAL TURBULENCE BOUNDARY LAYER
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作者 Wu Zheng Fudan University,Shanghai 200433,P.R.China 《Journal of Hydrodynamics》 SCIE EI CSCD 1990年第1期22-28,共7页
In this paper,the author first establishes the general finite difference formula for the governing equations of the turbulent average velocities in a steady two dimensional incompressible fluid boundary layer-inner la... In this paper,the author first establishes the general finite difference formula for the governing equations of the turbulent average velocities in a steady two dimensional incompressible fluid boundary layer-inner layer.Next, three key parameters of the difference scheme are determined respectively by several simple flow models with known analytical solutions.Finally a special five points difference system is given and its application value is showed by a numerical example for the vertical velocity distribution in an Ekman's layer. 展开更多
关键词 ON THE finite difference methods FOR TWO DIMENSIONAL TURBULENCE BOUNDARY LAYER very
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Optimal l~∞ error estimates of finite difference methods for the coupled Gross-Pitaevskii equations in high dimensions 被引量:11
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作者 WANG TingChun ZHAO XiaoFei 《Science China Mathematics》 SCIE 2014年第10期2189-2214,共26页
Due to the difficulty in obtaining the a priori estimate,it is very hard to establish the optimal point-wise error bound of a finite difference scheme for solving a nonlinear partial differential equation in high dime... Due to the difficulty in obtaining the a priori estimate,it is very hard to establish the optimal point-wise error bound of a finite difference scheme for solving a nonlinear partial differential equation in high dimensions(2D or 3D).We here propose and analyze finite difference methods for solving the coupled GrossPitaevskii equations in two dimensions,which models the two-component Bose-Einstein condensates with an internal atomic Josephson junction.The methods which we considered include two conservative type schemes and two non-conservative type schemes.Discrete conservation laws and solvability of the schemes are analyzed.For the four proposed finite difference methods,we establish the optimal convergence rates for the error at the order of O(h^2+τ~2)in the l~∞-norm(i.e.,the point-wise error estimates)with the time stepτand the mesh size h.Besides the standard techniques of the energy method,the key techniques in the analysis is to use the cut-off function technique,transformation between the time and space direction and the method of order reduction.All the methods and results here are also valid and can be easily extended to the three-dimensional case.Finally,numerical results are reported to confirm our theoretical error estimates for the numerical methods. 展开更多
关键词 coupled Gross-Pitaevskii equations finite difference method SOLVABILITY conservation laws pointwise convergence optimal error estimates
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Efficient Finite Difference/Spectral Method for the Time Fractional Ito Equation Using Fast Fourier Transform Technic
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作者 Dakang Cen Zhibo Wang Seakweng Vong 《Communications on Applied Mathematics and Computation》 EI 2023年第4期1591-1600,共10页
A finite difference/spectral scheme is proposed for the time fractional Ito equation.The mass conservation and stability of the numerical solution are deduced by the energy method in the L^(2)norm form.To reduce the c... A finite difference/spectral scheme is proposed for the time fractional Ito equation.The mass conservation and stability of the numerical solution are deduced by the energy method in the L^(2)norm form.To reduce the computation costs,the fast Fourier transform technic is applied to a pair of equivalent coupled differential equations.The effectiveness of the proposed algorithm is verified by the first numerical example.The mass conservation property and stability statement are confirmed by two other numerical examples. 展开更多
关键词 Time fractional Ito equation finite difference method Spectral method STABILITY
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Numerical Study by Imposing the Finite Difference Method for Unsteady Casson Fluid Flow with Heat Flux
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作者 Ali H. Tedjani 《Journal of Applied Mathematics and Physics》 2023年第12期3826-3839,共14页
This article presents an investigation into the flow and heat transfer characteristics of an impermeable stretching sheet subjected to Magnetohydrodynamic Casson fluid. The study considers the influence of slip veloci... This article presents an investigation into the flow and heat transfer characteristics of an impermeable stretching sheet subjected to Magnetohydrodynamic Casson fluid. The study considers the influence of slip velocity, thermal radiation conditions, and heat flux. The investigation is conducted employing a robust numerical method that accounts for the impact of thermal radiation. This category of fluid is apt for characterizing the movement of blood within an industrial artery, where the flow can be regulated by a material designed to manage it. The resolution of the ensuing system of ordinary differential equations (ODEs), representing the described problem, is accomplished through the application of the finite difference method. The examination of flow and heat transfer characteristics, including aspects such as unsteadiness, radiation parameter, slip velocity, Casson parameter, and Prandtl number, is explored and visually presented through tables and graphs to illustrate their impact. On the stretching sheet, calculations, and descriptions of the local skin-friction coefficient and the local Nusselt number are conducted. In conclusion, the findings indicate that the proposed method serves as a straightforward and efficient tool for exploring the solutions of fluid models of this kind. 展开更多
关键词 Casson Model Unsteady Stretching Sheet Variable Heat Flux MHD Slip Impacts Thermal Radiation finite difference Method
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Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals 被引量:1
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作者 Wenzhen Qu Hongwei Gao Yan Gu 《Advances in Applied Mathematics and Mechanics》 SCIE 2021年第6期1398-1417,共20页
In this paper,a high-accuracy numerical scheme is developed for long-time dynamic simulations of 2D and 3D wave propagation phenomena.In the derivation of the present approach,the second order time derivative of the p... In this paper,a high-accuracy numerical scheme is developed for long-time dynamic simulations of 2D and 3D wave propagation phenomena.In the derivation of the present approach,the second order time derivative of the physical quantity in the wave equation is treated as a substitution variable.Based on the temporal discretization with the Krylov deferred correction(KDC)technique,the original wave problem is then converted into the modified Helmholtz equation.The transformed boundary value problem(BVP)in space is efficiently simulated by using the meshless generalized finite difference method(GFDM)with Taylor series after truncating the second and fourth order approximations.The developed scheme is finally verified by four numerical experiments including cases with complicated domains or the temporally piecewise defined source function.Numerical results match with the analytical solutions and results by the COMSOL software,which demonstrates that the developed KDC-GFDM can allow large time-step sizes for wave propagation problems in longtime intervals. 展开更多
关键词 Wave equation Krylov deferred correction technique large time-step long-time simulation generalized finite difference method
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Stability and Time-Step Constraints of Implicit-Explicit Runge-Kutta Methods for the Linearized Korteweg-de Vries Equation
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作者 Joseph Hunter Zheng Sun Yulong Xing 《Communications on Applied Mathematics and Computation》 EI 2024年第1期658-687,共30页
This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either... This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints. 展开更多
关键词 Linearized Korteweg-de Vries(KdV)equation Implicit-explicit(IMEX)Runge-Kutta(RK)method STABILITY Courant-Friedrichs-Lewy(CFL)condition finite difference(FD)method Local discontinuous Galerkin(DG)method
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Asymptotic Behavior of the Finite Difference and the Finite Element Methods for Parabolic Equations
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作者 LIU Yang FENG Hui 《Wuhan University Journal of Natural Sciences》 EI CAS 2005年第6期953-956,共4页
The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are... The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continnous time. 展开更多
关键词 asymptotic behavior finite difference method finite element method EIGENVALUE
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An GPU accelerated finite difference method for heat transfer simulation
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作者 ZHOU Yi HE Fazhi QIU Yimin 《Computer Aided Drafting,Design and Manufacturing》 2013年第1期27-31,共5页
The heat transfer mathematic models are widely used in iron and steel industry area. Many computational models that represent this physical process is based on finite difference methods. The simulation of these phenom... The heat transfer mathematic models are widely used in iron and steel industry area. Many computational models that represent this physical process is based on finite difference methods. The simulation of these phenomena demands a high computa- tional cost. In this paper we employ GPU for the development of algorithm for a two-dimensional heat transfer problem with f'mite difference methods. The performance evaluation has been made and the comparison between CPU and GPU were discussed. The experimental result shows that GPU can solve this problem more efficiently when we need to divide calculation material into a large number of meshes. 展开更多
关键词 finite difference methods GPU Heat transfer OPENCL
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Improved finite difference method for pressure distribution of aerostatic bearing 被引量:4
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作者 郑书飞 蒋书运 《Journal of Southeast University(English Edition)》 EI CAS 2009年第4期501-505,共5页
An improved finite difference method (FDM)is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aero... An improved finite difference method (FDM)is described to solve existing problems such as low efficiency and poor convergence performance in the traditional method adopted to derive the pressure distribution of aerostatic bearings. A detailed theoretical analysis of the pressure distribution of the orifice-compensated aerostatic journal bearing is presented. The nonlinear dimensionless Reynolds equation of the aerostatic journal bearing is solved by the finite difference method. Based on the principle of flow equilibrium, a new iterative algorithm named the variable step size successive approximation method is presented to adjust the pressure at the orifice in the iterative process and enhance the efficiency and convergence performance of the algorithm. A general program is developed to analyze the pressure distribution of the aerostatic journal bearing by Matlab tool. The results show that the improved finite difference method is highly effective, reliable, stable, and convergent. Even when very thin gas film thicknesses (less than 2 Win)are considered, the improved calculation method still yields a result and converges fast. 展开更多
关键词 aerostatic bearing: pressure distribution: Reynolds equation: finite difference method: variable step size
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Using finite difference method to simulate casting thermal stress 被引量:6
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作者 Liao Dunming Zhang Bin +2 位作者 Zhou Jianxin Liu Ruixiang Chen Liliang 《China Foundry》 SCIE CAS 2011年第2期177-181,共5页
Thermal stress simulation can provide a scientific reference to eliminate defects such as crack,residual stress centralization and deformation etc.,caused by thermal stress during casting solidification.To study the t... Thermal stress simulation can provide a scientific reference to eliminate defects such as crack,residual stress centralization and deformation etc.,caused by thermal stress during casting solidification.To study the thermal stress distribution during casting process,a unilateral thermal-stress coupling model was employed to simulate 3D casting stress using Finite Difference Method(FDM),namely all the traditional thermal-elastic-plastic equations are numerically and differentially discrete.A FDM/FDM numerical simulation system was developed to analyze temperature and stress fields during casting solidification process.Two practical verifications were carried out,and the results from simulation basically coincided with practical cases.The results indicated that the FDM/FDM stress simulation system can be used to simulate the formation of residual stress,and to predict the occurrence of hot tearing.Because heat transfer and stress analysis are all based on FDM,they can use the same FD model,which can avoid the matching process between different models,and hence reduce temperature-load transferring errors.This approach makes the simulation of fluid flow,heat transfer and stress analysis unify into one single model. 展开更多
关键词 thermal stress numerical simulation finite difference method (FDM) casting solidification process
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Finite difference method for dynamic response analysis of anchorage system 被引量:5
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作者 言志信 段建 +3 位作者 江平 刘子振 赵红亮 黄文贵 《Journal of Central South University》 SCIE EI CAS 2014年第3期1098-1106,共9页
Based on some assumptions, the dynamic analysis model of anchorage system is established. The dynamic governing equation is expressed as finite difference format and programmed by using MATLAB language. Compared with ... Based on some assumptions, the dynamic analysis model of anchorage system is established. The dynamic governing equation is expressed as finite difference format and programmed by using MATLAB language. Compared with theoretical method, the finite difference method has been verified to be feasible by a case study. It is found that under seismic loading, the dynamic response of anchorage system is synchronously fluctuated with the seismic vibration. The change of displacement amplitude of material points is slight, and comparatively speaking, the displacement amplitude of the outside point is a little larger than that of the inside point, which shows amplification effect of surface. While the axial force amplitude transforms considerably from the inside to the outside. It increases first and reaches the peak value in the intersection between the anchoring section and free section, then decreases slowly in the free section. When considering damping effect of anchorage system, the finite difference method can reflect the time attenuation characteristic better, and the calculating result would be safer and more reasonable than the dynamic steady-state theoretical method. What is more, the finite difference method can be applied to the dynamic response analysis of harmonic and seismic random vibration for all kinds of anchor, and hence has a broad application prospect. 展开更多
关键词 anchorage system dynamic response finite difference method attenuation characteristic
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An explicit finite element-finite difference method for analyzing the effect of visco-elastic local topography on the earthquake motion 被引量:6
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作者 李小军 廖振鹏 关慧敏 《Acta Seismologica Sinica(English Edition)》 CSCD 1995年第3期447-456,共10页
An explicit finite element-finite difference method for analyzing the effects of two-dimensional visco-elastic localtopography on earthquake ground motion is prOPosed in this paper. In the method, at first, the finite... An explicit finite element-finite difference method for analyzing the effects of two-dimensional visco-elastic localtopography on earthquake ground motion is prOPosed in this paper. In the method, at first, the finite elementdiscrete model is formed by using the artificial boundary and finite element method, and the dynamic equationsof local nodes in the discrete model are obtained according to the theory of the special finite element method similar to the finite difference method, and then the explicit step-by-step integration formulas are presented by usingthe explicit difference method for solving the visco-elastic dynamic equation and Generalized Multi-transmittingBoundary. The method has the advantages of saving computing time and computer memory space, and it is suitable for any case of topography and has high computing accuracy and good computing stability. 展开更多
关键词 VISCO-ELASTIC seismic response finite difference method explicit finite element artificial boundary
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Implicit finite difference method for fractional percolation equation with Dirichlet and fractional boundary conditions 被引量:4
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作者 Boling GUO Qiang XU Zhe YIN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2016年第3期403-416,共14页
An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation (FPE) with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for ... An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation (FPE) with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for two special cases, i.e., a continued seep- age flow with a monotone percolation coefficient and a seepage flow with the fractional Neumann boundary condition. The accuracy and efficiency of the method are checked with two numerical examples. 展开更多
关键词 fractional percolation equation (FPE) Riemann-Liouville derivative frac-tional boundary condition finite difference method stability and convergence Toeplitzmatrix
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