This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes,e.g.,wave-propagation or heat-transfer,that are modeled by wave equations or heat equations.Here,we stu...This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes,e.g.,wave-propagation or heat-transfer,that are modeled by wave equations or heat equations.Here,we study both parabolic and hyperbolic equations.We focus on ADI (alternating direction implicit) methods and LOD (locally one-dimensional) methods,which are standard splitting methods of lower order,e.g.second-order.Our aim is to develop higher-order ADI methods,which are performed by Richardson extrapolation,Crank-Nicolson methods and higher-order LOD methods,based on locally higher-order methods.We discuss the new theoretical results of the stability and consistency of the ADI methods.The main idea is to apply a higher- order time discretization and combine it with the ADI methods.We also discuss the dis- cretization and splitting methods for first-order and second-order evolution equations. The stability analysis is given for the ADI method for first-order time derivatives and for the LOD (locally one-dimensional) methods for second-order time derivatives.The higher-order methods are unconditionally stable.Some numerical experiments verify our results.展开更多
In this paper the liquid argon nanojet break-up phenomenon was studied using the molecular dynamics method. The effects of temperature, nozzle diameter and body force on the nanojet break-up length and time were simu-...In this paper the liquid argon nanojet break-up phenomenon was studied using the molecular dynamics method. The effects of temperature, nozzle diameter and body force on the nanojet break-up length and time were simu- lated. Meanwhile, the particle size, wave length and the frequency of the disturbance were compared with the re- suits of linear stability analysis. The results showed that even though the fluid becomes discontinuous, the tradi- tional linear stability analysis can be used to make a rough calculation of the nanojet break-up.展开更多
In this paper, a new lattice hydrodynamic model is proposed by incorporating the driver anticipation effect of next-nearest-neighbor site. The linear stability analysis and nonlinear analysis show that the driver anti...In this paper, a new lattice hydrodynamic model is proposed by incorporating the driver anticipation effect of next-nearest-neighbor site. The linear stability analysis and nonlinear analysis show that the driver anticipation effect of next-nearest-neighbor site can enlarge the stable area of traffic flow. The space can be divided into three regions： stab/e, metastable, and unstable. Numerical simulation further illuminates that the driver anticipation effect of the next-neaxest-neighbor site can stabilize tramc flow in our modified lattice model, which is consistent with the analytical results.展开更多
文摘This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes,e.g.,wave-propagation or heat-transfer,that are modeled by wave equations or heat equations.Here,we study both parabolic and hyperbolic equations.We focus on ADI (alternating direction implicit) methods and LOD (locally one-dimensional) methods,which are standard splitting methods of lower order,e.g.second-order.Our aim is to develop higher-order ADI methods,which are performed by Richardson extrapolation,Crank-Nicolson methods and higher-order LOD methods,based on locally higher-order methods.We discuss the new theoretical results of the stability and consistency of the ADI methods.The main idea is to apply a higher- order time discretization and combine it with the ADI methods.We also discuss the dis- cretization and splitting methods for first-order and second-order evolution equations. The stability analysis is given for the ADI method for first-order time derivatives and for the LOD (locally one-dimensional) methods for second-order time derivatives.The higher-order methods are unconditionally stable.Some numerical experiments verify our results.
文摘In this paper the liquid argon nanojet break-up phenomenon was studied using the molecular dynamics method. The effects of temperature, nozzle diameter and body force on the nanojet break-up length and time were simu- lated. Meanwhile, the particle size, wave length and the frequency of the disturbance were compared with the re- suits of linear stability analysis. The results showed that even though the fluid becomes discontinuous, the tradi- tional linear stability analysis can be used to make a rough calculation of the nanojet break-up.
基金Supported by the Key Project of Chinese Ministry of Education under Grant No.211123the Scientific Research Fund of Hunan Provincial Education Department under Grant No.10B072+2 种基金Doctor Scientific Research Startup Project Foundation of Hunan University of Arts and Science under Grant No.BSQD1010the Fund of Key Construction Academic Subject of Hunan Provincethe Natural Science Foundation of Hunan Province under Grant No.14JJ2125
文摘In this paper, a new lattice hydrodynamic model is proposed by incorporating the driver anticipation effect of next-nearest-neighbor site. The linear stability analysis and nonlinear analysis show that the driver anticipation effect of next-nearest-neighbor site can enlarge the stable area of traffic flow. The space can be divided into three regions： stab/e, metastable, and unstable. Numerical simulation further illuminates that the driver anticipation effect of the next-neaxest-neighbor site can stabilize tramc flow in our modified lattice model, which is consistent with the analytical results.
