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
Implicit-explicit （IMEX） linear multistep methods are popular techniques for solving partial differential equations （PDEs） with terms of different types. While fixed timestep versions of such schemes have been dev...Implicit-explicit （IMEX） linear multistep methods are popular techniques for solving partial differential equations （PDEs） with terms of different types. While fixed timestep versions of such schemes have been developed and studied, implicit-explicit schemes also naturally arise in general situations where the temporal smoothness of the solution changes. In this paper we consider easily implementable variable step-size implicit-explicit （VSIMEX） linear multistep methods for time-dependent PDEs. Families of order-p, pstep VSIMEX schemes are constructed and analyzed, where p ranges from 1 to 4. The corresponding schemes are simple to implement and have the property that they reduce to the classical IMEX schemes whenever constant time step-sizes are imposed. The methods are validated on the Burgers＇ equation. These results demonstrate that by varying the time step-size, VSIMEX methods can outperform their fixed time step counterparts while still maintaining good numerical behavior.展开更多
综合电力系统(integrated power system,IPS)包含3/12相双绕组发电机等特殊高阶非线性元件,现有电力系统电磁暂态仿真软件均不提供其仿真模型。为此,采用隐式梯形法对双绕组发电机数学模型进行差分离散化处理,通过定、转子分离迭代,推...综合电力系统(integrated power system,IPS)包含3/12相双绕组发电机等特殊高阶非线性元件,现有电力系统电磁暂态仿真软件均不提供其仿真模型。为此,采用隐式梯形法对双绕组发电机数学模型进行差分离散化处理,通过定、转子分离迭代,推导出电机等效电路模型,并在PSCAD中建立双绕组发电机仿真模型。应用时步保持算法,将模型的仿真时步划分为计算时步和保持时步,提高了计算速度。最后,构建综合电力推进系统试验平台,发电机空载短路、推进系统调速的试验与仿真结果吻合,验证了建模方法的有效性和所建模型的正确性。研究表明,基于隐式梯形–时步保持算法的建模方法能够准确高效地建立双绕组发电机的仿真模型,可应用于EMTP类仿真软件,并可推广至IPS各类多相电机建模。展开更多
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 an NSERC Canada Postgraduate Scholarshipsupported by a grant from NSERC Canada
文摘Implicit-explicit （IMEX） linear multistep methods are popular techniques for solving partial differential equations （PDEs） with terms of different types. While fixed timestep versions of such schemes have been developed and studied, implicit-explicit schemes also naturally arise in general situations where the temporal smoothness of the solution changes. In this paper we consider easily implementable variable step-size implicit-explicit （VSIMEX） linear multistep methods for time-dependent PDEs. Families of order-p, pstep VSIMEX schemes are constructed and analyzed, where p ranges from 1 to 4. The corresponding schemes are simple to implement and have the property that they reduce to the classical IMEX schemes whenever constant time step-sizes are imposed. The methods are validated on the Burgers＇ equation. These results demonstrate that by varying the time step-size, VSIMEX methods can outperform their fixed time step counterparts while still maintaining good numerical behavior.
文摘综合电力系统(integrated power system,IPS)包含3/12相双绕组发电机等特殊高阶非线性元件,现有电力系统电磁暂态仿真软件均不提供其仿真模型。为此,采用隐式梯形法对双绕组发电机数学模型进行差分离散化处理,通过定、转子分离迭代,推导出电机等效电路模型,并在PSCAD中建立双绕组发电机仿真模型。应用时步保持算法,将模型的仿真时步划分为计算时步和保持时步,提高了计算速度。最后,构建综合电力推进系统试验平台,发电机空载短路、推进系统调速的试验与仿真结果吻合,验证了建模方法的有效性和所建模型的正确性。研究表明,基于隐式梯形–时步保持算法的建模方法能够准确高效地建立双绕组发电机的仿真模型,可应用于EMTP类仿真软件,并可推广至IPS各类多相电机建模。
