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
For real-time dynamic substructure testing(RTDST),the influence of the inertia force of fluid specimens on the stability and accuracy of the integration algorithms has never been investigated.Therefore,this study prop...For real-time dynamic substructure testing(RTDST),the influence of the inertia force of fluid specimens on the stability and accuracy of the integration algorithms has never been investigated.Therefore,this study proposes to investigate the stability and accuracy of the central difference method(CDM)for RTDST considering the specimen mass participation coefficient.First,the theory of the CDM for RTDST is presented.Next,the stability and accuracy of the CDM for RTDST considering the specimen mass participation coefficient are investigated.Finally,numerical simulations and experimental tests are conducted for verifying the effectiveness of the method.The study indicates that the stability of the algorithm is affected by the mass participation coefficient of the specimen,and the stability limit first increases and then decreases as the mass participation coefficient increases.In most cases,the mass participation coefficient will increase the stability limit of the algorithm,but in specific circumstances,the algorithm may lose its stability.The stability and accuracy of the CDM considering the mass participation coefficient are verified by numerical simulations and experimental tests on a three-story frame structure with a tuned liquid damper.展开更多
The possibility of using a nodal method allowing irregular distribution of nodes in a natural way is one of the main advantages of the generalized finite difference method (GFDM) with regard to the classical finite di...The possibility of using a nodal method allowing irregular distribution of nodes in a natural way is one of the main advantages of the generalized finite difference method (GFDM) with regard to the classical finite difference method. Moreover, this feature has made it one of the most-promising meshless methods because it also allows us to reduce the time-consuming task of mesh generation and the numerical solution of integrals. This characteristic allows us to shape geological features easily whilst maintaining accuracy in the results, which can be a source of great interest when dealing with this kind of problems. Two widespread geophysical investigation methods in civil engineering are the cross-hole method and the seismic refraction method. This paper shows the use of the GFDM to model the aforementioned geophysical investigation tests showing precision in the obtained results when comparing them with experimental data.展开更多
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
The value of form factor k at different drafts is important in predicting full-scale total resistance and speed for different types of ships. In the ITTC community, most organizations predict form factor k using a low...The value of form factor k at different drafts is important in predicting full-scale total resistance and speed for different types of ships. In the ITTC community, most organizations predict form factor k using a low-speed model test. However, this method is problematic for ships with bulbous bows and transom. In this article, a Computational Fluid Dynamics(CFD)-based method is introduced to obtain k for different type of ships at different drafts, and a comparison is made between the CFD method and the model test. The results show that the CFD method produces reasonable k values. A grid generating method and turbulence model are briefly discussed in the context of obtaining a consistent k using CFD.展开更多
A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite differen...A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.展开更多
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
In modelling elastic wave propagation in a porous medium, when the ratio between the fluid viscosity and the medium permeability is comparatively large, the stiffness problem of Blot＇s poroelastic equations will be e...In modelling elastic wave propagation in a porous medium, when the ratio between the fluid viscosity and the medium permeability is comparatively large, the stiffness problem of Blot＇s poroelastic equations will be encountered. In the paper, a partition method is developed to solve the stiffness problem with a staggered high-order finite-difference. The method splits the Biot equations into two systems. One is stiff, and solved analytically, the other is nonstiff, and solved numerically by using a high-order staggered-grid finite-difference scheme. The time step is determined by the staggered finite-difference algorithm in solving the nonstiff equations, thus a coarse time step may be employed. Therefore, the computation efficiency and computational stability are improved greatly. Also a perfect by matched layer technology is used in the split method as absorbing boundary conditions. The numerical results are compared with the analytical results and those obtained from the conventional staggered-grid finite-difference method in a homogeneous model, respectively. They are in good agreement with each other. Finally, a slightly more complex model is investigated and compared with related equivalent model to illustrate the good performance of the staggered-grid finite-difference scheme in the partition method.展开更多
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
In this study, the method of lines (MOLs) with higher order central difference approximation method coupled with the classical fourth order Runge-Kutta (RK(4,4)) method is used in solving shallow water equations (SWEs...In this study, the method of lines (MOLs) with higher order central difference approximation method coupled with the classical fourth order Runge-Kutta (RK(4,4)) method is used in solving shallow water equations (SWEs) in Cartesian coordinates to foresee water levels associated with a storm accurately along the coast of Bangladesh. In doing so, the partial derivatives of the SWEs with respect to the space variables were discretized with 5-point central difference, as a test case, to obtain a system of ordinary differential equations with time as an independent variable for every spatial grid point, which with initial conditions were solved by the RK(4,4) method. The complex land-sea interface and bottom topographic details were incorporated closely using nested schemes. The coastal and island boundaries were rectangularized through proper stair step representation, and the storing positions of the scalar and momentum variables were specified according to the rules of structured C-grid. A stable tidal regime was made over the model domain considering the effect of the major tidal constituent, M2 along the southern open boundary of the outermost parent scheme. The Meghna River fresh water discharge was taken into account for the inner most child scheme. To take into account the dynamic interaction of tide and surge, the generated tidal regime was introduced as the initial state of the sea, and the surge was then made to come over it through computer simulation. Numerical experiments were performed with the cyclone April 1991 to simulate water levels due to tide, surge, and their interaction at different stations along the coast of Bangladesh. Our computed results were found to compare reasonable well with the limited observed data obtained from Bangladesh Inland Water Transport Authority (BIWTA) and were found to be better in comparison with the results obtained through the regular finite difference method and the 3-point central difference MOLs coupled with the RK(4,4) method with regard to the root mean square error values.展开更多
Some superconvergence results of generalized difference solution for elliptic boundary value problem are given. It is shown that optimal points of the stresses for generalized difference method are the same as that fo...Some superconvergence results of generalized difference solution for elliptic boundary value problem are given. It is shown that optimal points of the stresses for generalized difference method are the same as that for finite element method.展开更多
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
A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is ...A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.展开更多
Using a discretized finite difference method, a numerical model was developed to study the interaction of regular waves with a perforated breakwater. Considering a non-viscous, non-rotational fluid, the governing equa...Using a discretized finite difference method, a numerical model was developed to study the interaction of regular waves with a perforated breakwater. Considering a non-viscous, non-rotational fluid, the governing equations of Laplacian velocity potential were developed, and specific conditions for every single boundary were defined. The final developed model was evaluated based on an existing experimental result. The evaluated model was used to simulate the condition for various wave periods from 0.6 to 2 s. The reflection coefficient and transmission coefficient of waves were examined with different breakwater porosities, wave steepnesses, and angular frequencies. The results show that the developed model can suitably present the effect of the structural and hydraulic parameters on the reflection and transmission coefficients. It was also found that with the increase in wave steepness, the reflection coefficient increased logarithmically, while the transmission coefficient decreased logarithmically.展开更多
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
In this paper, we consider two methods, the Second order Central Difference Method (SCDM) and the Finite Element Method (FEM) with P1 triangular elements, for solving two dimensional general linear Elliptic Partial Di...In this paper, we consider two methods, the Second order Central Difference Method (SCDM) and the Finite Element Method (FEM) with P1 triangular elements, for solving two dimensional general linear Elliptic Partial Differential Equations (PDE) with mixed derivatives along with Dirichlet and Neumann boundary conditions. These two methods have almost the same accuracy from theoretical aspect with regular boundaries, but generally Finite Element Method produces better approximations when the boundaries are irregular. In order to investigate which method produces better results from numerical aspect, we apply these methods into specific examples with regular boundaries with constant step-size for both of them. The results which obtained confirm, in most of the cases, the theoretical results.展开更多
The ground penetrating radar(GPR) forward simulation all aims at the singular and regular models, such as sandwich model, round cavity, square cavity, and so on, which are comparably simple. But as to the forward of c...The ground penetrating radar(GPR) forward simulation all aims at the singular and regular models, such as sandwich model, round cavity, square cavity, and so on, which are comparably simple. But as to the forward of curl interface underground or “v” figure complex model, it is difficult to realize. So it is important to forward the complex geoelectricity model. This paper takes two Maxwell’s vorticity equations as departure point, makes use of the principles of Yee’s space grid model theory and the basic principle finite difference time domain method, and deduces a GPR forward system of equation of two dimensional spaces. The Mur super absorbed boundary condition is adopted to solve the super strong reflection on the interceptive boundary when there is the forward simulation. And a self-made program is used to process forward simulation to two typical geoelectricity model.展开更多
基金supported by the Key Laboratory of Road Construction Technology and Equipment(Chang’an University,No.300102253502)the Natural Science Foundation of Shandong Province of China(GrantNo.ZR2022YQ06)the Development Plan of Youth Innovation Team in Colleges and Universities of Shandong Province(Grant No.2022KJ140).
文摘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.
基金National Natural Science Foundation of China under Grant Nos.51978213 and 51778190the National Key Research and Development Program of China under Grant Nos.2017YFC0703605 and 2016YFC0701106。
文摘For real-time dynamic substructure testing(RTDST),the influence of the inertia force of fluid specimens on the stability and accuracy of the integration algorithms has never been investigated.Therefore,this study proposes to investigate the stability and accuracy of the central difference method(CDM)for RTDST considering the specimen mass participation coefficient.First,the theory of the CDM for RTDST is presented.Next,the stability and accuracy of the CDM for RTDST considering the specimen mass participation coefficient are investigated.Finally,numerical simulations and experimental tests are conducted for verifying the effectiveness of the method.The study indicates that the stability of the algorithm is affected by the mass participation coefficient of the specimen,and the stability limit first increases and then decreases as the mass participation coefficient increases.In most cases,the mass participation coefficient will increase the stability limit of the algorithm,but in specific circumstances,the algorithm may lose its stability.The stability and accuracy of the CDM considering the mass participation coefficient are verified by numerical simulations and experimental tests on a three-story frame structure with a tuned liquid damper.
基金The authors acknowledge the support of the Escuela Tecnica Superior de Ingenieros Industriales(UNED)of Spain,project 2019-IFC02of the Universidad Politecnica de Madrid(UPM)(Research groups 2019).
文摘The possibility of using a nodal method allowing irregular distribution of nodes in a natural way is one of the main advantages of the generalized finite difference method (GFDM) with regard to the classical finite difference method. Moreover, this feature has made it one of the most-promising meshless methods because it also allows us to reduce the time-consuming task of mesh generation and the numerical solution of integrals. This characteristic allows us to shape geological features easily whilst maintaining accuracy in the results, which can be a source of great interest when dealing with this kind of problems. Two widespread geophysical investigation methods in civil engineering are the cross-hole method and the seismic refraction method. This paper shows the use of the GFDM to model the aforementioned geophysical investigation tests showing precision in the obtained results when comparing them with experimental data.
基金The National Natural Science Foundation of China(No50475073,50775036)the High Technology Research Program of Jiangsu Province(NoBG2006035)
文摘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.
基金Supported by Ministry of Industry and Information(No.K24097)
文摘The value of form factor k at different drafts is important in predicting full-scale total resistance and speed for different types of ships. In the ITTC community, most organizations predict form factor k using a low-speed model test. However, this method is problematic for ships with bulbous bows and transom. In this article, a Computational Fluid Dynamics(CFD)-based method is introduced to obtain k for different type of ships at different drafts, and a comparison is made between the CFD method and the model test. The results show that the CFD method produces reasonable k values. A grid generating method and turbulence model are briefly discussed in the context of obtaining a consistent k using CFD.
基金the National Natural Science Foundation of China
文摘A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.
文摘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.
基金Project supported by the ＂100 Talents Project＂ of the Chinese Academy of Sciences and the Major Program of the National Natural Science Foundation of China （Grant No 10534040）.
文摘In modelling elastic wave propagation in a porous medium, when the ratio between the fluid viscosity and the medium permeability is comparatively large, the stiffness problem of Blot＇s poroelastic equations will be encountered. In the paper, a partition method is developed to solve the stiffness problem with a staggered high-order finite-difference. The method splits the Biot equations into two systems. One is stiff, and solved analytically, the other is nonstiff, and solved numerically by using a high-order staggered-grid finite-difference scheme. The time step is determined by the staggered finite-difference algorithm in solving the nonstiff equations, thus a coarse time step may be employed. Therefore, the computation efficiency and computational stability are improved greatly. Also a perfect by matched layer technology is used in the split method as absorbing boundary conditions. The numerical results are compared with the analytical results and those obtained from the conventional staggered-grid finite-difference method in a homogeneous model, respectively. They are in good agreement with each other. Finally, a slightly more complex model is investigated and compared with related equivalent model to illustrate the good performance of the staggered-grid finite-difference scheme in the partition method.
基金supported by the National Natural Science Foundation of China(Nos.11171193 and11371229)the Natural Science Foundation of Shandong Province(No.ZR2014AM033)the Science and Technology Development Project of Shandong Province(No.2012GGB01198)
文摘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.
文摘In this study, the method of lines (MOLs) with higher order central difference approximation method coupled with the classical fourth order Runge-Kutta (RK(4,4)) method is used in solving shallow water equations (SWEs) in Cartesian coordinates to foresee water levels associated with a storm accurately along the coast of Bangladesh. In doing so, the partial derivatives of the SWEs with respect to the space variables were discretized with 5-point central difference, as a test case, to obtain a system of ordinary differential equations with time as an independent variable for every spatial grid point, which with initial conditions were solved by the RK(4,4) method. The complex land-sea interface and bottom topographic details were incorporated closely using nested schemes. The coastal and island boundaries were rectangularized through proper stair step representation, and the storing positions of the scalar and momentum variables were specified according to the rules of structured C-grid. A stable tidal regime was made over the model domain considering the effect of the major tidal constituent, M2 along the southern open boundary of the outermost parent scheme. The Meghna River fresh water discharge was taken into account for the inner most child scheme. To take into account the dynamic interaction of tide and surge, the generated tidal regime was introduced as the initial state of the sea, and the surge was then made to come over it through computer simulation. Numerical experiments were performed with the cyclone April 1991 to simulate water levels due to tide, surge, and their interaction at different stations along the coast of Bangladesh. Our computed results were found to compare reasonable well with the limited observed data obtained from Bangladesh Inland Water Transport Authority (BIWTA) and were found to be better in comparison with the results obtained through the regular finite difference method and the 3-point central difference MOLs coupled with the RK(4,4) method with regard to the root mean square error values.
基金This work is supported by the Foundatiorl of Zhongshan University Advanced Research Centre
文摘Some superconvergence results of generalized difference solution for elliptic boundary value problem are given. It is shown that optimal points of the stresses for generalized difference method are the same as that for finite element method.
基金Projects(51308273,41372307,41272326) supported by the National Natural Science Foundation of ChinaProjects(2010(A)06-b) supported by Science and Technology Fund of Yunan Provincial Communication Department,China
文摘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.
基金supported by the Yunnan Provincial Applied Basic Research Program of China(No. KKSY201207019)
文摘A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.
文摘Using a discretized finite difference method, a numerical model was developed to study the interaction of regular waves with a perforated breakwater. Considering a non-viscous, non-rotational fluid, the governing equations of Laplacian velocity potential were developed, and specific conditions for every single boundary were defined. The final developed model was evaluated based on an existing experimental result. The evaluated model was used to simulate the condition for various wave periods from 0.6 to 2 s. The reflection coefficient and transmission coefficient of waves were examined with different breakwater porosities, wave steepnesses, and angular frequencies. The results show that the developed model can suitably present the effect of the structural and hydraulic parameters on the reflection and transmission coefficients. It was also found that with the increase in wave steepness, the reflection coefficient increased logarithmically, while the transmission coefficient decreased logarithmically.
基金supported by the National Natural Science Foundation of China (No.50805056)New Century Excellent Talents in University (No.NCET-09-0396)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,Ministry of Education (2009)
文摘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.
文摘In this paper, we consider two methods, the Second order Central Difference Method (SCDM) and the Finite Element Method (FEM) with P1 triangular elements, for solving two dimensional general linear Elliptic Partial Differential Equations (PDE) with mixed derivatives along with Dirichlet and Neumann boundary conditions. These two methods have almost the same accuracy from theoretical aspect with regular boundaries, but generally Finite Element Method produces better approximations when the boundaries are irregular. In order to investigate which method produces better results from numerical aspect, we apply these methods into specific examples with regular boundaries with constant step-size for both of them. The results which obtained confirm, in most of the cases, the theoretical results.
文摘The ground penetrating radar(GPR) forward simulation all aims at the singular and regular models, such as sandwich model, round cavity, square cavity, and so on, which are comparably simple. But as to the forward of curl interface underground or “v” figure complex model, it is difficult to realize. So it is important to forward the complex geoelectricity model. This paper takes two Maxwell’s vorticity equations as departure point, makes use of the principles of Yee’s space grid model theory and the basic principle finite difference time domain method, and deduces a GPR forward system of equation of two dimensional spaces. The Mur super absorbed boundary condition is adopted to solve the super strong reflection on the interceptive boundary when there is the forward simulation. And a self-made program is used to process forward simulation to two typical geoelectricity model.
