To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical c...To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.展开更多
A method combining finite difference method(FDM)and k-means clustering algorithm which can determine the threshold of rock bridge generation is proposed.Jointed slope models with different joint coalescence coefficien...A method combining finite difference method(FDM)and k-means clustering algorithm which can determine the threshold of rock bridge generation is proposed.Jointed slope models with different joint coalescence coefficients(k)are constructed based on FDM.The rock bridge area was divided through k-means algorithm and the optimal number of clusters was determined by sum of squared errors(SSE)and elbow method.The influence of maximum principal stress and stress change rate as clustering indexes on the clustering results of rock bridges was compared by using Euclidean distance.The results show that using stress change rate as clustering index is more effective.When the joint coalescence coefficient is less than 0.6,there is no significant stress concentration in the middle area of adjacent joints,that is,no generation of rock bridge.In addition,the range of rock bridge is affected by the coalescence coefficient(k),the relative position of joints and the parameters of weak interlayer.展开更多
This study investigates the complex heat transfer dynamics inmultilayer bifacial photovoltaic(bPV)solar modules under spectrally resolved solar irradiation.A novel numericalmodel is developed to incorporate internal h...This study investigates the complex heat transfer dynamics inmultilayer bifacial photovoltaic(bPV)solar modules under spectrally resolved solar irradiation.A novel numericalmodel is developed to incorporate internal heat generation resulting from optical absorption,grounded in the physical equations governing light-matter interactions within the module’smultilayer structure.The model accounts for reflection and transmission at each interface between adjacent layers,as well as absorption within individual layers,using the wavelength-dependent dielectric properties of constituent materials.These properties are used to calculate the spectral reflectance,transmittance,and absorption coefficients,enabling precise quantification of internal heat sources from irradiance incidents on both the front and rear surfaces of the module.The study further examines the influence of irradiance reflection on thermal behavior,evaluates the thermal impact of various supporting materials placed beneath the module,and analyzes the role of albedo in modifying heat distribution.By incorporating spectrally resolved heat generation across each layer often simplified or omitted in conventional models,the proposed approach enhances physical accuracy.The transient heat equation is solved using a one-dimensional finite difference(FD)method to produce detailed temperature profiles under multiple operating scenarios,including Standard Test Conditions(STC),Bifacial Standard Test Conditions(BSTC),Normal Operating Cell Temperature(NOCT),and Bifacial NOCT(BNOCT).The results offer valuable insights into the interplay between optical and thermal phenomena in bifacial systems,informing the design and optimization of more efficient photovoltaic technologies.展开更多
In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving th...In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving the convergence of the one-point large deviations rate function (LDRF) of the spatial FDM, which is about the asymptotical limit of a parametric variational problem. The main idea for proving the convergence of the LDRF of the spatial FDM is via the Γ-convergence of objective functions. This relies on the qualitative analysis of skeleton equations of the original equation and the numerical method. In order to overcome the difficulty that the drift coefficient is not one-sided Lipschitz continuous, we derive the equivalent characterization of the skeleton equation of the spatial FDM and the discrete interpolation inequality to obtain the uniform boundedness of the solution to the underlying skeleton equation. These play important roles in deriving the T-convergence of objective functions.展开更多
Accurately simulating water flow movement in vadose zone is crucial for effective water resources assessment.Richards'equation,which describes the movement of water flow in the vadose zone,is highly nonlinear and ...Accurately simulating water flow movement in vadose zone is crucial for effective water resources assessment.Richards'equation,which describes the movement of water flow in the vadose zone,is highly nonlinear and challenging to solve.Existing numerical methods often face issues such as numerical dispersion,oscillation,and mass non-conservation when spatial and temporal discretization conditions are not appropriately configured.To address these problems and achieve accurate and stable numerical solutions,a finite analytic method based on water content-based Richards'equation(FAM-W)is proposed.The performance of the FAM-W is compared with analytical solutions,Finite Difference Method(FDM),and Finite Analytic Method based on the pressure Head-based Richards'equation(FAM-H).Compared to analytical solution and other numerical methods(FDM and FAM-H),FAM-W demonstrates superior accuracy and efficiency in controlling mass balance errors,regardless of spatial step sizes.This study introduces a novel approach for modelling water flow in the vadose zone,offering significant benefits for water resources management.展开更多
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
In this paper,we give improved error estimates for linearized and nonlinear CrankNicolson type finite difference schemes of Ginzburg-Landau equation in two dimensions.For linearized Crank-Nicolson scheme,we use mathem...In this paper,we give improved error estimates for linearized and nonlinear CrankNicolson type finite difference schemes of Ginzburg-Landau equation in two dimensions.For linearized Crank-Nicolson scheme,we use mathematical induction to get unconditional error estimates in discrete L^(2)and H^(1)norm.However,it is not applicable for the nonlinear scheme.Thus,based on a‘cut-off’function and energy analysis method,we get unconditional L^(2)and H^(1)error estimates for the nonlinear scheme,as well as boundedness of numerical solutions.In addition,if the assumption for exact solutions is improved compared to before,unconditional and optimal pointwise error estimates can be obtained by energy analysis method and several Sobolev inequalities.Finally,some numerical examples are given to verify our theoretical analysis.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
Contact bounce of relay, which is the main cause of electric abrasion and material erosion, is inevitable. By using the mode expansion form, the dynamic behavior of two different reed systems for aerospace relays is a...Contact bounce of relay, which is the main cause of electric abrasion and material erosion, is inevitable. By using the mode expansion form, the dynamic behavior of two different reed systems for aerospace relays is analyzed. The dynamic model uses Euler-Bernoulli beam theory for cantilever beam, in which the driving force (or driving moment) of the electromagnetic system is taken into account, and the contact force between moving contact and stationary contact is simulated by the Kelvin-Voigt vis-coelastic...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
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
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
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
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 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
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
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
Surface subsidence induced by underground mining is a typical serious geohazard.Numerical approaches such as the discrete element method(DEM)and finite difference method(FDM)have been widely used to model and analyze ...Surface subsidence induced by underground mining is a typical serious geohazard.Numerical approaches such as the discrete element method(DEM)and finite difference method(FDM)have been widely used to model and analyze mining-induced surface subsidence.However,the DEM is typically computationally expensive,and is not capable of analyzing large-scale problems,while the mesh distortion may occur in the FDM modeling of largely deformed surface subsidence.To address the above problems,this paper presents a geometrically and locally adaptive remeshing method for the FDM modeling of largely deformed surface subsidence induced by underground mining.The essential ideas behind the proposed method are as follows:(i)Geometrical features of elements(i.e.the mesh quality),rather than the calculation errors,are employed as the indicator for determining whether to conduct the remeshing;and(ii)Distorted meshes with multiple attributes,rather than those with only a single attribute,are locally regenerated.In the proposed method,the distorted meshes are first adaptively determined based on the mesh quality,and then removed from the original mesh model.The tetrahedral mesh in the distorted area is first regenerated,and then the physical field variables of old mesh are transferred to the new mesh.The numerical calculation process recovers when finishing the regeneration and transformation.To verify the effectiveness of the proposed method,the surface deformation of the Yanqianshan iron mine,Liaoning Province,China,is numerically investigated by utilizing the proposed method,and compared with the numerical results of the DEM modeling.Moreover,the proposed method is applied to predicting the surface subsidence in Anjialing No.1 Underground Mine,Shanxi Province,China.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
基金Supported by Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)+3 种基金National Natural Science Foundation of China(12301556)Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)Basic Research Plan of Shanxi Province(202203021211129)。
文摘To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.
基金supported by the National Natural Science Foundation of China(No.42277175)Guangxi Emergency Management Department 2024 Innovation and Technology Research Project,China(No.2024GXYJ006)+2 种基金Hunan Provincial Department of Natural Resources Geological Exploration Project,China(No.2023ZRBSHZ056)The First National Natural Disaster Comprehensive Risk Survey in Hunan Province,China(No.2022-70)Guizhou Provincial Major Scientific and Technological Program,China(No.2023-425).
文摘A method combining finite difference method(FDM)and k-means clustering algorithm which can determine the threshold of rock bridge generation is proposed.Jointed slope models with different joint coalescence coefficients(k)are constructed based on FDM.The rock bridge area was divided through k-means algorithm and the optimal number of clusters was determined by sum of squared errors(SSE)and elbow method.The influence of maximum principal stress and stress change rate as clustering indexes on the clustering results of rock bridges was compared by using Euclidean distance.The results show that using stress change rate as clustering index is more effective.When the joint coalescence coefficient is less than 0.6,there is no significant stress concentration in the middle area of adjacent joints,that is,no generation of rock bridge.In addition,the range of rock bridge is affected by the coalescence coefficient(k),the relative position of joints and the parameters of weak interlayer.
文摘This study investigates the complex heat transfer dynamics inmultilayer bifacial photovoltaic(bPV)solar modules under spectrally resolved solar irradiation.A novel numericalmodel is developed to incorporate internal heat generation resulting from optical absorption,grounded in the physical equations governing light-matter interactions within the module’smultilayer structure.The model accounts for reflection and transmission at each interface between adjacent layers,as well as absorption within individual layers,using the wavelength-dependent dielectric properties of constituent materials.These properties are used to calculate the spectral reflectance,transmittance,and absorption coefficients,enabling precise quantification of internal heat sources from irradiance incidents on both the front and rear surfaces of the module.The study further examines the influence of irradiance reflection on thermal behavior,evaluates the thermal impact of various supporting materials placed beneath the module,and analyzes the role of albedo in modifying heat distribution.By incorporating spectrally resolved heat generation across each layer often simplified or omitted in conventional models,the proposed approach enhances physical accuracy.The transient heat equation is solved using a one-dimensional finite difference(FD)method to produce detailed temperature profiles under multiple operating scenarios,including Standard Test Conditions(STC),Bifacial Standard Test Conditions(BSTC),Normal Operating Cell Temperature(NOCT),and Bifacial NOCT(BNOCT).The results offer valuable insights into the interplay between optical and thermal phenomena in bifacial systems,informing the design and optimization of more efficient photovoltaic technologies.
基金supported by the National Natural Science Foundation of China(12201228,12171047)the Fundamental Research Funds for the Central Universities(3034011102)supported by National Key R&D Program of China(2020YFA0713701).
文摘In this work, we first derive the one-point large deviations principle (LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method (FDM). Then, we focus on giving the convergence of the one-point large deviations rate function (LDRF) of the spatial FDM, which is about the asymptotical limit of a parametric variational problem. The main idea for proving the convergence of the LDRF of the spatial FDM is via the Γ-convergence of objective functions. This relies on the qualitative analysis of skeleton equations of the original equation and the numerical method. In order to overcome the difficulty that the drift coefficient is not one-sided Lipschitz continuous, we derive the equivalent characterization of the skeleton equation of the spatial FDM and the discrete interpolation inequality to obtain the uniform boundedness of the solution to the underlying skeleton equation. These play important roles in deriving the T-convergence of objective functions.
基金supported by the National Natural Science Foundation of China(No.42372287 and No.U24A20178)the Fundamental Research Funds for the Central Universities CHD(No.2024SHEEAR002)+3 种基金the Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shaanxi Province(No.2020024)the China Postdoctoral Science Foundation(GZC20232955,2024M753472,and 2024MD763937)the Science-Technology Foundation for Young Scientists of Gansu Province,China(No.24JRRA097)the Study of biodiversity survey and limiting factor analysis of Yinkentala(2023ZL01).
文摘Accurately simulating water flow movement in vadose zone is crucial for effective water resources assessment.Richards'equation,which describes the movement of water flow in the vadose zone,is highly nonlinear and challenging to solve.Existing numerical methods often face issues such as numerical dispersion,oscillation,and mass non-conservation when spatial and temporal discretization conditions are not appropriately configured.To address these problems and achieve accurate and stable numerical solutions,a finite analytic method based on water content-based Richards'equation(FAM-W)is proposed.The performance of the FAM-W is compared with analytical solutions,Finite Difference Method(FDM),and Finite Analytic Method based on the pressure Head-based Richards'equation(FAM-H).Compared to analytical solution and other numerical methods(FDM and FAM-H),FAM-W demonstrates superior accuracy and efficiency in controlling mass balance errors,regardless of spatial step sizes.This study introduces a novel approach for modelling water flow in the vadose zone,offering significant benefits for water resources management.
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Supported by the National Natural Science Foundation of China(Grant No.11571181)the Research Start-Up Foundation of Nantong University(Grant No.135423602051).
文摘In this paper,we give improved error estimates for linearized and nonlinear CrankNicolson type finite difference schemes of Ginzburg-Landau equation in two dimensions.For linearized Crank-Nicolson scheme,we use mathematical induction to get unconditional error estimates in discrete L^(2)and H^(1)norm.However,it is not applicable for the nonlinear scheme.Thus,based on a‘cut-off’function and energy analysis method,we get unconditional L^(2)and H^(1)error estimates for the nonlinear scheme,as well as boundedness of numerical solutions.In addition,if the assumption for exact solutions is improved compared to before,unconditional and optimal pointwise error estimates can be obtained by energy analysis method and several Sobolev inequalities.Finally,some numerical examples are given to verify our theoretical analysis.
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.
文摘Contact bounce of relay, which is the main cause of electric abrasion and material erosion, is inevitable. By using the mode expansion form, the dynamic behavior of two different reed systems for aerospace relays is analyzed. The dynamic model uses Euler-Bernoulli beam theory for cantilever beam, in which the driving force (or driving moment) of the electromagnetic system is taken into account, and the contact force between moving contact and stationary contact is simulated by the Kelvin-Voigt vis-coelastic...
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.
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.
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.
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.
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.
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supported by the National Natural Science Foundation of China(Grant Nos.11602235 and 41772326)the Fundamental Research Funds for the Central Universities of China(Grant No.2652018091)。
文摘Surface subsidence induced by underground mining is a typical serious geohazard.Numerical approaches such as the discrete element method(DEM)and finite difference method(FDM)have been widely used to model and analyze mining-induced surface subsidence.However,the DEM is typically computationally expensive,and is not capable of analyzing large-scale problems,while the mesh distortion may occur in the FDM modeling of largely deformed surface subsidence.To address the above problems,this paper presents a geometrically and locally adaptive remeshing method for the FDM modeling of largely deformed surface subsidence induced by underground mining.The essential ideas behind the proposed method are as follows:(i)Geometrical features of elements(i.e.the mesh quality),rather than the calculation errors,are employed as the indicator for determining whether to conduct the remeshing;and(ii)Distorted meshes with multiple attributes,rather than those with only a single attribute,are locally regenerated.In the proposed method,the distorted meshes are first adaptively determined based on the mesh quality,and then removed from the original mesh model.The tetrahedral mesh in the distorted area is first regenerated,and then the physical field variables of old mesh are transferred to the new mesh.The numerical calculation process recovers when finishing the regeneration and transformation.To verify the effectiveness of the proposed method,the surface deformation of the Yanqianshan iron mine,Liaoning Province,China,is numerically investigated by utilizing the proposed method,and compared with the numerical results of the DEM modeling.Moreover,the proposed method is applied to predicting the surface subsidence in Anjialing No.1 Underground Mine,Shanxi Province,China.
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.
