A new variable time step method,which is called the backwards calculating time step method,is presented in this paper.It allows numerical simulation of soil freezing and thawing while avoiding "phase change missi...A new variable time step method,which is called the backwards calculating time step method,is presented in this paper.It allows numerical simulation of soil freezing and thawing while avoiding "phase change missing and overflowing".A sensitive heat capacity model is introduced through which the calculation errors are analyzed.Then the equation using the self-adjusted time step is presented and solved using finite differences.Through this equation,the time needed for a space cell to reach the phase change point temperature is calculated.Using this time allows the time step to be adjusted so that errors caused by "phase change missing and overflowing" are successfully eliminated.Above all,the obvious features of this method are an accelerated rate for adjusting the time step and simplifing the computations.An actual example proves that this method can accurately calculate the temperature fields during soil freezing and thawing.It is an improvement over traditional methods and can be widely used on complicated multi-dimensional phase change problems.展开更多
This paper presents a method for directly analyzing the stability of complex-DDEs on the basis of stability switches. Two novel criteria are developed for the stability of a class of complex- DDEs. These results not o...This paper presents a method for directly analyzing the stability of complex-DDEs on the basis of stability switches. Two novel criteria are developed for the stability of a class of complex- DDEs. These results not only generalize some known results in literature but also greatly reduce the complexity of analysis and computation. To validate the effectiveness of the proposed criteria, the stabilization problem of the extended time delay auto-synchronization （ETDAS） control and n time delay auto-synchronization （NTDAS） control are then further investigated, respectively. The numerical simulations are consistent with the above theoretical analysis.展开更多
基金Project 2006G1662-00 supported by the Key Science and Technology Project of Heilongjiang Province
文摘A new variable time step method,which is called the backwards calculating time step method,is presented in this paper.It allows numerical simulation of soil freezing and thawing while avoiding "phase change missing and overflowing".A sensitive heat capacity model is introduced through which the calculation errors are analyzed.Then the equation using the self-adjusted time step is presented and solved using finite differences.Through this equation,the time needed for a space cell to reach the phase change point temperature is calculated.Using this time allows the time step to be adjusted so that errors caused by "phase change missing and overflowing" are successfully eliminated.Above all,the obvious features of this method are an accelerated rate for adjusting the time step and simplifing the computations.An actual example proves that this method can accurately calculate the temperature fields during soil freezing and thawing.It is an improvement over traditional methods and can be widely used on complicated multi-dimensional phase change problems.
基金This work was supported by National＇Science Foundation for Distinguished Young Scholars under Grant No. 10825207, and in part by Foundation for the Author of National Excellent Doctoral Dissertation of China under Grant No. 200430.
文摘This paper presents a method for directly analyzing the stability of complex-DDEs on the basis of stability switches. Two novel criteria are developed for the stability of a class of complex- DDEs. These results not only generalize some known results in literature but also greatly reduce the complexity of analysis and computation. To validate the effectiveness of the proposed criteria, the stabilization problem of the extended time delay auto-synchronization （ETDAS） control and n time delay auto-synchronization （NTDAS） control are then further investigated, respectively. The numerical simulations are consistent with the above theoretical analysis.
