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
A balanced adaptive time-stepping strategy is implemented in an implicit discontinuous Galerkin solver to guarantee the temporal accuracy of unsteady simulations.A proper relation between the spatial,temporal and iter...A balanced adaptive time-stepping strategy is implemented in an implicit discontinuous Galerkin solver to guarantee the temporal accuracy of unsteady simulations.A proper relation between the spatial,temporal and iterative errors generated within one time step is constructed.With an estimate of temporal and spatial error using an embedded RungeKutta scheme and a higher order spatial discretization,an adaptive time-stepping strategy is proposed based on the idea that the time step should be the maximum without obviously infuencing the total error of the discretization.The designed adaptive time-stepping strategy is then tested in various types of problems including isentropic vortex convection,steady-state fow past a fat plate,Taylor-Green vortex and turbulent fow over a circular cylinder at Re=3900.The results indicate that the adaptive time-stepping strategy can maintain that the discretization error is dominated by the spatial error and relatively high efciency is obtained for unsteady and steady,well-resolved and under-resolved simulations.展开更多
A generalized solution scheme using implicit time integrators for piecewise linear and nonlinear systems is developed.The piecewise linear characteristic has been well‐discussed in previous studies,in which the origi...A generalized solution scheme using implicit time integrators for piecewise linear and nonlinear systems is developed.The piecewise linear characteristic has been well‐discussed in previous studies,in which the original problem has been transformed into linear complementarity problems(LCPs)and then solved via the Lemke algorithm for each time step.The proposed scheme,instead,uses the projection function to describe the discontinuity in the dynamics equations,and solves for each step the nonlinear equations obtained from the implicit integrator by the semismooth Newton iteration.Compared with the LCP‐based scheme,the new scheme offers a more general choice by allowing other nonlinearities in the governing equations.To assess its performances,several illustrative examples are solved.The numerical solutions demonstrate that the new scheme can not only predict satisfactory results for piecewise nonlinear systems,but also exhibits substantial efficiency advantages over the LCP‐based scheme when applied to piecewise linear systems.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Zhen-Guo Yan acknowledges supports from the National Natural Science Foundation of China(Grant no.11902344)National Numerical Windtunnel Project.The development of the implicit solver in Nektar++has been supported by EPSRC grant(EP/R029423/1)UK Turbulence Consortium grant(EP/R029326/1).
文摘A balanced adaptive time-stepping strategy is implemented in an implicit discontinuous Galerkin solver to guarantee the temporal accuracy of unsteady simulations.A proper relation between the spatial,temporal and iterative errors generated within one time step is constructed.With an estimate of temporal and spatial error using an embedded RungeKutta scheme and a higher order spatial discretization,an adaptive time-stepping strategy is proposed based on the idea that the time step should be the maximum without obviously infuencing the total error of the discretization.The designed adaptive time-stepping strategy is then tested in various types of problems including isentropic vortex convection,steady-state fow past a fat plate,Taylor-Green vortex and turbulent fow over a circular cylinder at Re=3900.The results indicate that the adaptive time-stepping strategy can maintain that the discretization error is dominated by the spatial error and relatively high efciency is obtained for unsteady and steady,well-resolved and under-resolved simulations.
文摘A generalized solution scheme using implicit time integrators for piecewise linear and nonlinear systems is developed.The piecewise linear characteristic has been well‐discussed in previous studies,in which the original problem has been transformed into linear complementarity problems(LCPs)and then solved via the Lemke algorithm for each time step.The proposed scheme,instead,uses the projection function to describe the discontinuity in the dynamics equations,and solves for each step the nonlinear equations obtained from the implicit integrator by the semismooth Newton iteration.Compared with the LCP‐based scheme,the new scheme offers a more general choice by allowing other nonlinearities in the governing equations.To assess its performances,several illustrative examples are solved.The numerical solutions demonstrate that the new scheme can not only predict satisfactory results for piecewise nonlinear systems,but also exhibits substantial efficiency advantages over the LCP‐based scheme when applied to piecewise linear systems.
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。
