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
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
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
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
With more applications of seismic exploration in metal ore exploration,forward modelling of seismic wave has become more important in metal ore. Finite difference method and pseudo-spectral method are two important me...With more applications of seismic exploration in metal ore exploration,forward modelling of seismic wave has become more important in metal ore. Finite difference method and pseudo-spectral method are two important methods of wave-field simulation. Results of previous studies show that both methods have distinct advantages and disadvantages: Finite difference method has high precision but its dispersion is serious; pseudospectral method considers both computational efficiency and precision but has less precision than finite-difference. The authors consider the complex structural characteristics of the metal ore,furthermore add random media in order to simulate the complex effects produced by metal ore for wave field. First,the study introduced the theories of random media and two forward modelling methods. Second,it compared the simulation results of two methods on fault model. Then the authors established a complex metal ore model,added random media and compared computational efficiency and precision. As a result,it is found that finite difference method is better than pseudo-spectral method in precision and boundary treatment,but the computational efficiency of pseudospectral method is slightly higher than the finite difference method.展开更多
Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained result...Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.展开更多
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
In this paper we consider the numerical method of characteristics for the numerical solution of initial value problems (IVPs) for quasilinear hyperbolic Partial Differential Equations, as well as the difference scheme...In this paper we consider the numerical method of characteristics for the numerical solution of initial value problems (IVPs) for quasilinear hyperbolic Partial Differential Equations, as well as the difference scheme Central Time Central Space (CTCS), Crank-Nicolson scheme, ω scheme and the method of characteristics for the numerical solution of initial and boundary value prob-lems for the one-dimension homogeneous wave equation. The initial deriva-tive condition is approximated by different second order difference quotients in order to examine which gives more accurate numerical results. The local truncation error, consistency and stability of the difference schemes CTCS, Crank-Nicolson and ω are also considered.展开更多
Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly elliptic partial differential ...Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly elliptic partial differential problems. In this work, it is shown that the condition number of the resulting preconditioned system is bounded independently of both of the polynomial degrees used in the spectral element method and the element sizes. Several numerical tests verify the h-p independence of the proposed preconditioning.展开更多
Numerical simulation of complex flow fields with multi-scale structures is one of the most important and challenging branches of computational fluid dynamics. From linear analysis and numerical experiments it has been...Numerical simulation of complex flow fields with multi-scale structures is one of the most important and challenging branches of computational fluid dynamics. From linear analysis and numerical experiments it has been discovered that the higher-order accurate method can give reliable and efficient computational results, as well as better resolution of the complex flow fields with multi-scale structures. Compact finite difference schemes, which feature higher-order accuracy and spectral-like resolution with smaller stencils and easier application of boundary conditions, has attracted more and more interest and attention.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
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
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
文摘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.
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the National Natural Science Foundation of China under Grant Number NSFC 11801302Tsinghua University Initiative Scientific Research Program.Yang Yang is supported by the NSF Grant DMS-1818467.
文摘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.
文摘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.
基金Supported by the National"863"Project(No.2014AA06A605)
文摘With more applications of seismic exploration in metal ore exploration,forward modelling of seismic wave has become more important in metal ore. Finite difference method and pseudo-spectral method are two important methods of wave-field simulation. Results of previous studies show that both methods have distinct advantages and disadvantages: Finite difference method has high precision but its dispersion is serious; pseudospectral method considers both computational efficiency and precision but has less precision than finite-difference. The authors consider the complex structural characteristics of the metal ore,furthermore add random media in order to simulate the complex effects produced by metal ore for wave field. First,the study introduced the theories of random media and two forward modelling methods. Second,it compared the simulation results of two methods on fault model. Then the authors established a complex metal ore model,added random media and compared computational efficiency and precision. As a result,it is found that finite difference method is better than pseudo-spectral method in precision and boundary treatment,but the computational efficiency of pseudospectral method is slightly higher than the finite difference method.
文摘Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.
文摘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.
文摘In this paper we consider the numerical method of characteristics for the numerical solution of initial value problems (IVPs) for quasilinear hyperbolic Partial Differential Equations, as well as the difference scheme Central Time Central Space (CTCS), Crank-Nicolson scheme, ω scheme and the method of characteristics for the numerical solution of initial and boundary value prob-lems for the one-dimension homogeneous wave equation. The initial deriva-tive condition is approximated by different second order difference quotients in order to examine which gives more accurate numerical results. The local truncation error, consistency and stability of the difference schemes CTCS, Crank-Nicolson and ω are also considered.
文摘Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly elliptic partial differential problems. In this work, it is shown that the condition number of the resulting preconditioned system is bounded independently of both of the polynomial degrees used in the spectral element method and the element sizes. Several numerical tests verify the h-p independence of the proposed preconditioning.
文摘Numerical simulation of complex flow fields with multi-scale structures is one of the most important and challenging branches of computational fluid dynamics. From linear analysis and numerical experiments it has been discovered that the higher-order accurate method can give reliable and efficient computational results, as well as better resolution of the complex flow fields with multi-scale structures. Compact finite difference schemes, which feature higher-order accuracy and spectral-like resolution with smaller stencils and easier application of boundary conditions, has attracted more and more interest and attention.
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.
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(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.
