This research aims to solve Differential Algebraic Equation (DAE) problems in their original form, wherein both the differential and algebraic equations remain. The Newton or Newton-Broyden technique along with some i...This research aims to solve Differential Algebraic Equation (DAE) problems in their original form, wherein both the differential and algebraic equations remain. The Newton or Newton-Broyden technique along with some integrators such as the Runge-Kutta method is coupled together to solve the problems. Experiments show that the method developed in this paper is efficient, as it demonstrates that implementation of the method is not difficult, and such method is able to provide approximate solutions with ease within some desired accuracy standards.展开更多
Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are establi...Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.展开更多
为了解决电压稳定问题,基于电力系统动态分析的微分代数模型,提出了一种有效的动态稳定分析和失稳类型判别方法。利用带预测-校正步骤的延拓算法追踪平衡解流形,并采取考虑平衡解流形曲率大小的自适应策略控制步长,在平衡解流形曲率较...为了解决电压稳定问题,基于电力系统动态分析的微分代数模型,提出了一种有效的动态稳定分析和失稳类型判别方法。利用带预测-校正步骤的延拓算法追踪平衡解流形,并采取考虑平衡解流形曲率大小的自适应策略控制步长,在平衡解流形曲率较小处采用较大步长,而在平衡解流形曲率较大处采用较小步长;在计及元件动态特性的基础上,利用小扰动法在每个平衡点分析电力系统的动态稳定性,并用数值摄动法计算状态矩阵;利用状态变量的模式参与因子判断系统的动态失稳类型。使用本文所提方法对New England 10机39节点系统进行了仿真分析,实验结果证明了本方法的有效性和实用性。展开更多
Studies the different types of multistep discretization of index 3 differential-algebraic equations in Hessenberg form. Existense, uniqueness and influence of perturbations; Local convergence of multistep discretizati...Studies the different types of multistep discretization of index 3 differential-algebraic equations in Hessenberg form. Existense, uniqueness and influence of perturbations; Local convergence of multistep discretization; Details on the numerical tests.展开更多
The incompressible Navier-Stokes equations, upon spatial discretization, be- come a system of differential algebraic equations, formally of index 2. But due to the special forms of the discrete gradient and discrete d...The incompressible Navier-Stokes equations, upon spatial discretization, be- come a system of differential algebraic equations, formally of index 2. But due to the special forms of the discrete gradient and discrete divergence, its index can be regarded as 1. Thus, in this paper, a systematic approach following the ODE theory and methods is presented for the construction of high-order time-accurate implicit schemes for the incompressible Navier-Stokes equations, with projection methods for efficiency of numerical solution. The 3rd order 3-step BDF with component- consistent pressure-correction projection method is a first attempt in this direction; the related iterative solution of the auxiliary velocity the boundary conditions and the stability of the algorithm are discussed. Results of numerical tests on the incom- pressible Navier-Stokes equations with an exact solution are presented, confirming the accuracy stability and component- consistency of the proposed method.展开更多
This paper combines the implicit multistep method and the half explicit multistep method to solve index2 differentiaLalgebraic equations (DAEs), proposesthe predictor-corrector formula. This method enlarge the set of ...This paper combines the implicit multistep method and the half explicit multistep method to solve index2 differentiaLalgebraic equations (DAEs), proposesthe predictor-corrector formula. This method enlarge the set of multistep Inthodssuitable to solve index-2 DAEs and improve the mboum order of multistep methodfor solving index2 DAEs. This paPer discuss the global convergence and the im-plemellt of the method. Numerical test are also listed which show the method itproposed it better than BDF method when solving nonstiff DAEs.展开更多
文摘This research aims to solve Differential Algebraic Equation (DAE) problems in their original form, wherein both the differential and algebraic equations remain. The Newton or Newton-Broyden technique along with some integrators such as the Runge-Kutta method is coupled together to solve the problems. Experiments show that the method developed in this paper is efficient, as it demonstrates that implementation of the method is not difficult, and such method is able to provide approximate solutions with ease within some desired accuracy standards.
基金Project supported by the National Natural Science Foundation of China(No.11432010)the Doctoral Program Foundation of Education Ministry of China(No.20126102110023)+2 种基金the 111Project of China(No.B07050)the Fundamental Research Funds for the Central Universities(No.310201401JCQ01001)the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University(No.CX201517)
文摘Projected Runge-Kutta （R-K） methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations （DAEs） in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.
文摘为了解决电压稳定问题,基于电力系统动态分析的微分代数模型,提出了一种有效的动态稳定分析和失稳类型判别方法。利用带预测-校正步骤的延拓算法追踪平衡解流形,并采取考虑平衡解流形曲率大小的自适应策略控制步长,在平衡解流形曲率较小处采用较大步长,而在平衡解流形曲率较大处采用较小步长;在计及元件动态特性的基础上,利用小扰动法在每个平衡点分析电力系统的动态稳定性,并用数值摄动法计算状态矩阵;利用状态变量的模式参与因子判断系统的动态失稳类型。使用本文所提方法对New England 10机39节点系统进行了仿真分析,实验结果证明了本方法的有效性和实用性。
文摘Studies the different types of multistep discretization of index 3 differential-algebraic equations in Hessenberg form. Existense, uniqueness and influence of perturbations; Local convergence of multistep discretization; Details on the numerical tests.
文摘The incompressible Navier-Stokes equations, upon spatial discretization, be- come a system of differential algebraic equations, formally of index 2. But due to the special forms of the discrete gradient and discrete divergence, its index can be regarded as 1. Thus, in this paper, a systematic approach following the ODE theory and methods is presented for the construction of high-order time-accurate implicit schemes for the incompressible Navier-Stokes equations, with projection methods for efficiency of numerical solution. The 3rd order 3-step BDF with component- consistent pressure-correction projection method is a first attempt in this direction; the related iterative solution of the auxiliary velocity the boundary conditions and the stability of the algorithm are discussed. Results of numerical tests on the incom- pressible Navier-Stokes equations with an exact solution are presented, confirming the accuracy stability and component- consistency of the proposed method.
文摘This paper combines the implicit multistep method and the half explicit multistep method to solve index2 differentiaLalgebraic equations (DAEs), proposesthe predictor-corrector formula. This method enlarge the set of multistep Inthodssuitable to solve index-2 DAEs and improve the mboum order of multistep methodfor solving index2 DAEs. This paPer discuss the global convergence and the im-plemellt of the method. Numerical test are also listed which show the method itproposed it better than BDF method when solving nonstiff DAEs.
