In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales.We show by a combination of analytical arguments and numerical examp...In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales.We show by a combination of analytical arguments and numerical examples that implicit methods in general fail to capture the effective dynamics at the slow time scale.This is due to the fact that such implicit methods cannot correctly capture non-Dirac invariant distributions when the time step size is much larger than the relaxation time of the system.展开更多
This paper discusses a kind of implicit iterative methods with some variable parameters, which are called control parameters, for solving ill-posed operator equations. The theoretical results show that the new methods...This paper discusses a kind of implicit iterative methods with some variable parameters, which are called control parameters, for solving ill-posed operator equations. The theoretical results show that the new methods always lead to optimal convergence rates and have some other important features, especially the methods can be implemented parallelly.展开更多
The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF me...The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.展开更多
In this paper two implicit 2-step hybrid methods are proposed! one has order five, the other six. The stability properties of the methods are analysed. The 5th order method is proved to be A-stable and the 6th order o...In this paper two implicit 2-step hybrid methods are proposed! one has order five, the other six. The stability properties of the methods are analysed. The 5th order method is proved to be A-stable and the 6th order one is not, but still has a relatively large region of absolute stability. The implementation of the 5th order method is also discussed.展开更多
Natural gas hydrate, as a potential energy resource, deposits in permafrost and marine sediment with large quantities. The current exploitation methods include depressurization, thermal stimulation, and inhibitor inje...Natural gas hydrate, as a potential energy resource, deposits in permafrost and marine sediment with large quantities. The current exploitation methods include depressurization, thermal stimulation, and inhibitor injection. However, many issues have to be resolved before the commercial production. In the present study, a 2-D axisymmetric simulator for gas production from hydrate reservoirs is developed. The simulator includes equations of conductive and convective heat transfer, kinetic of hydrate decomposition, and multiphase flow. These equations are discretized based on the finite difference method and are solved with the fully implicit simultaneous solution method. The process of laboratory-scale hydrate decomposition by depressurization is simulated. For different surrounding temperatures and outlet pressures, time evolutions of gas and water generations during hydrate dissociation are evaluated, and variations of temperature, pressure, and multiphase fluid flow conditions are analyzed. The results suggest that the rate of heat transfer plays an important role in the process. Furthermore, high surrounding temperature and low outlet valve pressure may increase the rate of hydrate dissociation with insignificant impact on final cumulative gas volume.展开更多
We applied the projection and contraction method to nonlinear complementarity problem (NCP). Moveover, we proposed an inexact implicit method for (NCP) and proved the convergence.
This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditiona...This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai＇s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems.展开更多
In this paper,two classes of Riesz space fractional partial differential equations including space-fractional and space-time-fractional ones are considered.These two models can be regarded as the generalization of the...In this paper,two classes of Riesz space fractional partial differential equations including space-fractional and space-time-fractional ones are considered.These two models can be regarded as the generalization of the classical wave equation in two space dimensions.Combining with the Crank-Nicolson method in temporal direction,efficient alternating direction implicit Galerkin finite element methods for solving these two fractional models are developed,respectively.The corresponding stability and convergence analysis of the numerical methods are discussed.Numerical results are provided to verify the theoretical analysis.展开更多
This paper presents a quasi-static implicit generalized interpolation material point method(i GIMP)with B-bar approach for large deformation geotechnical problems.The i GIMP algorithm is an extension of the implicit m...This paper presents a quasi-static implicit generalized interpolation material point method(i GIMP)with B-bar approach for large deformation geotechnical problems.The i GIMP algorithm is an extension of the implicit material point method(iMPM).The global stiffness matrix is formed explicitly and the Newton-Raphson iterative method is used to solve the equilibrium equations.Where possible,the implementation procedure closely follows standard finite element method(FEM)approaches to allow easy conversion of other FEM codes.The generalized interpolation function is assigned to eliminate the inherent cell crossing noise within conventional MPM.For the first time,the B-bar approach is used to overcome volumetric locking in standard GIMP method for near-incompressible non-linear geomechanics.The proposed i GIMP was tested and compared with i MPM and analytical solutions via a 1 D column compression problem.Results highlighted the superiority of the i GIMP approach in reducing stress oscillations,thereby improving computational accuracy.Then,elasto-plastic slope stabilities and rigid footing problems were considered,further illustrating the ability of the proposed method to overcome volumetric locking due to incompressibility.Results showed that the proposed i GIMP with B-bar approach can be used to simulate geotechnical problems with large deformations.展开更多
Efficient solution techniques for high-order temporal and spatial discontinuous Galerkin（DG） discretizations of the unsteady Navier–Stokes equations are developed. A fourth-order implicit Runge–Kutta（IRK） scheme...Efficient solution techniques for high-order temporal and spatial discontinuous Galerkin（DG） discretizations of the unsteady Navier–Stokes equations are developed. A fourth-order implicit Runge–Kutta（IRK） scheme is applied for the time integration and a multigrid preconditioned GMRES solver is extended to solve the nonlinear system arising from each IRK stage. Several modifications to the implicit solver have been considered to achieve the efficiency enhancement and meantime to reduce the memory requirement. A variety of time-accurate viscous flow simulations are performed to assess the resulting high-order implicit DG methods. The designed order of accuracy for temporal discretization scheme is validate and the present implicit solver shows the superior performance by allowing quite large time step to be used in solving time-implicit systems. Numerical results are in good agreement with the published data and demonstrate the potential advantages of the high-order scheme in gaining both the high accuracy and the high efficiency.展开更多
It has been proven that the implicit method used to solve the vibration equation can be transformed into an explicit method,which is called the concomitant explicit method.The constant acceleration method's concom...It has been proven that the implicit method used to solve the vibration equation can be transformed into an explicit method,which is called the concomitant explicit method.The constant acceleration method's concomitant explicit method was used as an example and is described in detail in this paper.The relationship between the implicit method and explicit method is defined,which provides some guidance about how to create a new explicit method that has high precision and computational efficiency.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 the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear ...In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.展开更多
In this paper, the author applied an implicit iterative method to solve linear ill posed equations with both perturbed operators and perturbed data. After having carefully estimated some terms involved, a satisfactor...In this paper, the author applied an implicit iterative method to solve linear ill posed equations with both perturbed operators and perturbed data. After having carefully estimated some terms involved, a satisfactory order of convergence rate was derived.展开更多
Square piles of reinforced concrete(RC)in marine environments are susceptible to chloride-inducedcorrosion.A novel reverse-seepage technique(RST)is applied to square piles to block the intrusion of chlorides.Thisresea...Square piles of reinforced concrete(RC)in marine environments are susceptible to chloride-inducedcorrosion.A novel reverse-seepage technique(RST)is applied to square piles to block the intrusion of chlorides.Thisresearch introduces a computational model designed to predict the lifespan of corrosion initiation in reinforced concretesquare piles when applied reverse-seepage pressure.The model considers the impacts of chloride binding and the tripletime-dependence property among the permeability,the corrected surface chloride concentration,and the diffusioncoefficient.The proposed numerical model is solved using the alternating direction implicit(ADI)approach,and itsaccuracy and reliability are evaluated by contrasting the computational outcomes with the analytical solution andexperimental results.Furthermore,the primary factors contributing to the corrosion of reinforced concrete square pilesare analyzed.The results indicate that applying RST can decrease the chloride penetration depth and prolong the lifespanof corrosion initiation in square piles.The water-cement ratio and reverse seepage pressure are the most influentialfactors.A water pressure of 0.4 MPa can double the life of concrete,and the durable life of concrete with a water-cementratio of 0.3 can reach 100 years.展开更多
Electron emission plays a dominant role in plasma-cathode interactions and is a key factor in many plasma phenomena and industrial applications.It is necessary to illustrate the various electron emission mechanisms an...Electron emission plays a dominant role in plasma-cathode interactions and is a key factor in many plasma phenomena and industrial applications.It is necessary to illustrate the various electron emission mechanisms and the corresponding applicable description models to evaluate their impacts on discharge properties.In this study,detailed expressions of the simplified formulas valid for field emission to thermo-field emission to thermionic emission typically used in the numerical simulation are proposed,and the corresponding application ranges are determined in the framework of the Murphy-Good theory,which is commonly regarded as the general model and to be accurate in the full range of conditions of the validity of the theory.Dimensionless parameterization was used to evaluate the emission current density of the Murphy-Good formula,and a deviation factor was defined to obtain the application ranges for different work functions(2.5‒5 eV),cathode temperatures(300‒6000 K),and emitted electric fields(10^(5) to 10^(10) V·m^(-1)).The deviation factor was shown to be a nonmonotonic function of the three parameters.A comparative study of particle number densities in atmospheric gas discharge with a tungsten cathode was performed based on the one-dimensional implicit particle-in-cell(PIC)with the Monte Carlo collision(MCC)method according to the aforementioned application ranges.It was found that small differences in emission current density can lead to variations in the distributions of particle number density due to changes in the collisional environment.This study provides a theoretical basis for selecting emission models for subsequent numerical simulations.展开更多
Heat transfers due to MHD-conjugate free convection from the isothermal horizontal circular cylinder while viscosity is a function of temperature is investigated. The governing equations of the flow and connected boun...Heat transfers due to MHD-conjugate free convection from the isothermal horizontal circular cylinder while viscosity is a function of temperature is investigated. The governing equations of the flow and connected boundary conditions are made dimensionless using a set of non-dimensional parameters. The governing equations are solved numerically using the finite difference method. Numerical results are obtained for various values of viscosity variation parameter, Prandtl number, magnetic parameter, and conjugate conduction parameter for the velocity and the temperature within the boundary layer as well as the skin friction coefficients and heat transfer rate along the surface.展开更多
A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions a...A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions according to Reynolds number.In the far-wall region,the thermal melt flow was calculated as Newtonian flow.In the near-wall region,the thermal melt flow was calculated as non-Newtonian flow.It was proved that the new algorithm based on the projection method with the implicit technique was correct through nonparametric statistics method and experiment.The simulation results show that the new algorithm based on the projection method with the implicit technique calculates more quickly than the solution algorithm-volume of fluid method using the explicit difference method.展开更多
A model for the amount of pollution in lakes connected with some rivers is introduced.In this model,it is supposed the density of pollution in a lake has memory.The model leads to a system of fractional differential e...A model for the amount of pollution in lakes connected with some rivers is introduced.In this model,it is supposed the density of pollution in a lake has memory.The model leads to a system of fractional differential equations.This system is transformed into a system of Volterra integral equations with memory kernels.The existence and regularity of the solutions are investigated.A high-order numerical method is introduced and analyzed and compared with an explicit method based on the regularity of the solution.Validation examples are supported,and some models are simulated and discussed.展开更多
Several efficient analytical methods have been developed to solve the solid-state diffusion problem, for constant diffusion coefficient problems. However, these methods cannot be applied for concentration-dependent di...Several efficient analytical methods have been developed to solve the solid-state diffusion problem, for constant diffusion coefficient problems. However, these methods cannot be applied for concentration-dependent diffusion coefficient problems and numerical methods are used instead. Herein, grid-based numerical methods derived from the control volume discretization are presented to resolve the characteristic nonlinear system of partial differential equations. A novel hybrid backward Euler control volume (HBECV) method is presented which requires only one iteration to reach an implicit solution. The HBECV results are shown to be stable and accurate for a moderate number of grid points. The computational speed and accuracy of the HBECV, justify its use in battery simulations, in which the solid-state diffusion coefficient is a strong function of the concentration.展开更多
基金ONR grant N00014-01-0674.TLi is partially supported by National Science Foundation of China grants 10401004the National Basic Research Program under grant 2005CB321704.
文摘In this paper we study the behavior of a family of implicit numerical methods applied to stochastic differential equations with multiple time scales.We show by a combination of analytical arguments and numerical examples that implicit methods in general fail to capture the effective dynamics at the slow time scale.This is due to the fact that such implicit methods cannot correctly capture non-Dirac invariant distributions when the time step size is much larger than the relaxation time of the system.
基金This work was supported by the National Natural Science Foundation of China
文摘This paper discusses a kind of implicit iterative methods with some variable parameters, which are called control parameters, for solving ill-posed operator equations. The theoretical results show that the new methods always lead to optimal convergence rates and have some other important features, especially the methods can be implemented parallelly.
文摘The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.
文摘In this paper two implicit 2-step hybrid methods are proposed! one has order five, the other six. The stability properties of the methods are analysed. The 5th order method is proved to be A-stable and the 6th order one is not, but still has a relatively large region of absolute stability. The implementation of the 5th order method is also discussed.
基金supported by the National High Technology Research and Development Program of China(863 Program, Grant No.2006AA09A209-5)the National Natural Science Foundation of China (Key Program,Grant No.50736001)the Major Research Project of Ministry of Education of China (Grant No.306005)
文摘Natural gas hydrate, as a potential energy resource, deposits in permafrost and marine sediment with large quantities. The current exploitation methods include depressurization, thermal stimulation, and inhibitor injection. However, many issues have to be resolved before the commercial production. In the present study, a 2-D axisymmetric simulator for gas production from hydrate reservoirs is developed. The simulator includes equations of conductive and convective heat transfer, kinetic of hydrate decomposition, and multiphase flow. These equations are discretized based on the finite difference method and are solved with the fully implicit simultaneous solution method. The process of laboratory-scale hydrate decomposition by depressurization is simulated. For different surrounding temperatures and outlet pressures, time evolutions of gas and water generations during hydrate dissociation are evaluated, and variations of temperature, pressure, and multiphase fluid flow conditions are analyzed. The results suggest that the rate of heat transfer plays an important role in the process. Furthermore, high surrounding temperature and low outlet valve pressure may increase the rate of hydrate dissociation with insignificant impact on final cumulative gas volume.
基金Supported by the National Natural Science Foundation of China (No. 202001036)
文摘We applied the projection and contraction method to nonlinear complementarity problem (NCP). Moveover, we proposed an inexact implicit method for (NCP) and proved the convergence.
基金The project supported by the National Key Basic Research and Development Foundation of the Ministry of Science and Technology of China （G2000048702, 2003CB716707）the National Science Fund for Distinguished Young Scholars （10025208）+1 种基金 the National Natural Science Foundation of China （Key Program） （10532040） the Research Fund for 0versea Chinese （10228028）.
文摘This paper presents a new simple method of implicit time integration with two control parameters for solving initial-value problems of dynamics such that its accuracy is at least of order two along with the conditional and unconditional stability regions of the parameters. When the control parameters in the method are optimally taken in their regions, the accuracy may be improved to reach of order three. It is found that the new scheme can achieve lower numerical amplitude dissipation and period dispersion than some of the existing methods, e.g. the Newmark method and Zhai＇s approach, when the same time step size is used. The region of time step dependent on the parameters in the new scheme is explicitly obtained. Finally, some examples of dynamic problems are given to show the accuracy and efficiency of the proposed scheme applied in dynamic systems.
基金supported by the Guangxi Natural Science Foundation[grant numbers 2018GXNSFBA281020,2018GXNSFAA138121]the Doctoral Starting up Foundation of Guilin University of Technology[grant number GLUTQD2016044].
文摘In this paper,two classes of Riesz space fractional partial differential equations including space-fractional and space-time-fractional ones are considered.These two models can be regarded as the generalization of the classical wave equation in two space dimensions.Combining with the Crank-Nicolson method in temporal direction,efficient alternating direction implicit Galerkin finite element methods for solving these two fractional models are developed,respectively.The corresponding stability and convergence analysis of the numerical methods are discussed.Numerical results are provided to verify the theoretical analysis.
基金the National Natural Science Foundation of China(Nos.41807223 and 51908175)the Fundamental Research Funds for the Central Universities(No.B210202096)+1 种基金the Natural Science Foundation of Guangdong Province(No.2018A030310346)the Water Conservancy Science and Technology Innovation Project of Guangdong Province(No.2020-11),China。
文摘This paper presents a quasi-static implicit generalized interpolation material point method(i GIMP)with B-bar approach for large deformation geotechnical problems.The i GIMP algorithm is an extension of the implicit material point method(iMPM).The global stiffness matrix is formed explicitly and the Newton-Raphson iterative method is used to solve the equilibrium equations.Where possible,the implementation procedure closely follows standard finite element method(FEM)approaches to allow easy conversion of other FEM codes.The generalized interpolation function is assigned to eliminate the inherent cell crossing noise within conventional MPM.For the first time,the B-bar approach is used to overcome volumetric locking in standard GIMP method for near-incompressible non-linear geomechanics.The proposed i GIMP was tested and compared with i MPM and analytical solutions via a 1 D column compression problem.Results highlighted the superiority of the i GIMP approach in reducing stress oscillations,thereby improving computational accuracy.Then,elasto-plastic slope stabilities and rigid footing problems were considered,further illustrating the ability of the proposed method to overcome volumetric locking due to incompressibility.Results showed that the proposed i GIMP with B-bar approach can be used to simulate geotechnical problems with large deformations.
文摘Efficient solution techniques for high-order temporal and spatial discontinuous Galerkin（DG） discretizations of the unsteady Navier–Stokes equations are developed. A fourth-order implicit Runge–Kutta（IRK） scheme is applied for the time integration and a multigrid preconditioned GMRES solver is extended to solve the nonlinear system arising from each IRK stage. Several modifications to the implicit solver have been considered to achieve the efficiency enhancement and meantime to reduce the memory requirement. A variety of time-accurate viscous flow simulations are performed to assess the resulting high-order implicit DG methods. The designed order of accuracy for temporal discretization scheme is validate and the present implicit solver shows the superior performance by allowing quite large time step to be used in solving time-implicit systems. Numerical results are in good agreement with the published data and demonstrate the potential advantages of the high-order scheme in gaining both the high accuracy and the high efficiency.
基金Fundamental Research Funds for the Central Universities
文摘It has been proven that the implicit method used to solve the vibration equation can be transformed into an explicit method,which is called the concomitant explicit method.The constant acceleration method's concomitant explicit method was used as an example and is described in detail in this paper.The relationship between the implicit method and explicit method is defined,which provides some guidance about how to create a new explicit method that has high precision and computational efficiency.
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 Key Disciplines of Shanghai Municipality (Operations Research & Cybernetics, No. S30104)the Shanghai Leading Academic Discipline Project (No. J50101)
文摘In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.
文摘In this paper, the author applied an implicit iterative method to solve linear ill posed equations with both perturbed operators and perturbed data. After having carefully estimated some terms involved, a satisfactory order of convergence rate was derived.
基金Projects(52178371,52108355,52178321)supported by the National Natural Science Foundation of ChinaProject(202305)supported by the Research Project of Engineering Research Centre of Rock-Soil Drilling&Excavation and Protection,Ministry of Education,China。
文摘Square piles of reinforced concrete(RC)in marine environments are susceptible to chloride-inducedcorrosion.A novel reverse-seepage technique(RST)is applied to square piles to block the intrusion of chlorides.Thisresearch introduces a computational model designed to predict the lifespan of corrosion initiation in reinforced concretesquare piles when applied reverse-seepage pressure.The model considers the impacts of chloride binding and the tripletime-dependence property among the permeability,the corrected surface chloride concentration,and the diffusioncoefficient.The proposed numerical model is solved using the alternating direction implicit(ADI)approach,and itsaccuracy and reliability are evaluated by contrasting the computational outcomes with the analytical solution andexperimental results.Furthermore,the primary factors contributing to the corrosion of reinforced concrete square pilesare analyzed.The results indicate that applying RST can decrease the chloride penetration depth and prolong the lifespanof corrosion initiation in square piles.The water-cement ratio and reverse seepage pressure are the most influentialfactors.A water pressure of 0.4 MPa can double the life of concrete,and the durable life of concrete with a water-cementratio of 0.3 can reach 100 years.
基金supported in part by National Natural Science Foundation of China(Nos.52176087 and 52277164)Foundation for Innovative Research Groups of National Natural Science Foundation of China(No.51721004)+1 种基金Scientific Research Program Funded by Shaanxi Provincial Education Department(No.23JP115)Youth Innovation Team of Shaanxi Universities,in part by the Natural Science Basic Research Plan of Shaanxi Province(Nos.2021J Z-48 and 2020JM-462).
文摘Electron emission plays a dominant role in plasma-cathode interactions and is a key factor in many plasma phenomena and industrial applications.It is necessary to illustrate the various electron emission mechanisms and the corresponding applicable description models to evaluate their impacts on discharge properties.In this study,detailed expressions of the simplified formulas valid for field emission to thermo-field emission to thermionic emission typically used in the numerical simulation are proposed,and the corresponding application ranges are determined in the framework of the Murphy-Good theory,which is commonly regarded as the general model and to be accurate in the full range of conditions of the validity of the theory.Dimensionless parameterization was used to evaluate the emission current density of the Murphy-Good formula,and a deviation factor was defined to obtain the application ranges for different work functions(2.5‒5 eV),cathode temperatures(300‒6000 K),and emitted electric fields(10^(5) to 10^(10) V·m^(-1)).The deviation factor was shown to be a nonmonotonic function of the three parameters.A comparative study of particle number densities in atmospheric gas discharge with a tungsten cathode was performed based on the one-dimensional implicit particle-in-cell(PIC)with the Monte Carlo collision(MCC)method according to the aforementioned application ranges.It was found that small differences in emission current density can lead to variations in the distributions of particle number density due to changes in the collisional environment.This study provides a theoretical basis for selecting emission models for subsequent numerical simulations.
文摘Heat transfers due to MHD-conjugate free convection from the isothermal horizontal circular cylinder while viscosity is a function of temperature is investigated. The governing equations of the flow and connected boundary conditions are made dimensionless using a set of non-dimensional parameters. The governing equations are solved numerically using the finite difference method. Numerical results are obtained for various values of viscosity variation parameter, Prandtl number, magnetic parameter, and conjugate conduction parameter for the velocity and the temperature within the boundary layer as well as the skin friction coefficients and heat transfer rate along the surface.
基金Project (50975263) supported by the National Natural Science Foundation of ChinaProject (2010081015) supported by International Cooperation Project of Shanxi Province, China+1 种基金 Project (2010-78) supported by the Scholarship Council in Shanxi province, ChinaProject (2010420120005) supported by Doctoral Fund of Ministry of Education of China
文摘A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions according to Reynolds number.In the far-wall region,the thermal melt flow was calculated as Newtonian flow.In the near-wall region,the thermal melt flow was calculated as non-Newtonian flow.It was proved that the new algorithm based on the projection method with the implicit technique was correct through nonparametric statistics method and experiment.The simulation results show that the new algorithm based on the projection method with the implicit technique calculates more quickly than the solution algorithm-volume of fluid method using the explicit difference method.
文摘A model for the amount of pollution in lakes connected with some rivers is introduced.In this model,it is supposed the density of pollution in a lake has memory.The model leads to a system of fractional differential equations.This system is transformed into a system of Volterra integral equations with memory kernels.The existence and regularity of the solutions are investigated.A high-order numerical method is introduced and analyzed and compared with an explicit method based on the regularity of the solution.Validation examples are supported,and some models are simulated and discussed.
文摘Several efficient analytical methods have been developed to solve the solid-state diffusion problem, for constant diffusion coefficient problems. However, these methods cannot be applied for concentration-dependent diffusion coefficient problems and numerical methods are used instead. Herein, grid-based numerical methods derived from the control volume discretization are presented to resolve the characteristic nonlinear system of partial differential equations. A novel hybrid backward Euler control volume (HBECV) method is presented which requires only one iteration to reach an implicit solution. The HBECV results are shown to be stable and accurate for a moderate number of grid points. The computational speed and accuracy of the HBECV, justify its use in battery simulations, in which the solid-state diffusion coefficient is a strong function of the concentration.
