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 thickness of a broken zone, a state parameter of roadway surrounding rock, is used as the index to evaluate the stabi1ity of surrounding rock of a deep roadway. The paper gives a theoretic formula fo...In this paper the thickness of a broken zone, a state parameter of roadway surrounding rock, is used as the index to evaluate the stabi1ity of surrounding rock of a deep roadway. The paper gives a theoretic formula for calculating the thickness of the broken zone. The author points out that not only the ultimate strength of rockmass but its residual strength and strain-softening level all have a great influence on the stability of surrounding rock of a deep roadway. The paper’s results show that to reinforce surrounding rock, raise its residual strength and lower its strain-softening level should be taken as a basic requirement for supports of a deep roadway. In addition, the research also indicates that it is impossible for roadway supports to change surrounding rock states of a deep roadway, so it is certain for them to work in a broken state. For this reason, a sufficient yieldable quantity is necessary for roadway supports used in deep mining.展开更多
In the Xiaowan arch dam there are massive temperature cracks nearly parallel to the dam axis. Obviously, whether the cracks may spread or not during the water storage process is one of the crucial factors for the safe...In the Xiaowan arch dam there are massive temperature cracks nearly parallel to the dam axis. Obviously, whether the cracks may spread or not during the water storage process is one of the crucial factors for the safety of a dam. In this paper, a new type of crack element, in which the contact component is implicitly included into the concrete component, is proposed to simulate the effects of the existing cracks. The crack element is proved by numerical example to share the merits of both conventional contact elements and joint elements. With a finite element model of the cracked arch dam together with its rock foundation established, the transient displacement and stress fields of the dam are obtained. The complicated rock foundation, the construction process of the arch dam, the massive cracks, the transient temperature field, as well as the water storage process have been taken into consideration in the simulation. In addition to the global model, several sub-models for typical crack tips are also generated with finer elements placed around the tips. Thus, more accurate displacement and stress distribution are obtained by simultaneous sub-model simulation. Based on the calculation of stress intensity factor for crack tips by extension method, the temperature cracks in the Xiaowan arch dam are finally proved to be stable.展开更多
We consider the mean-square stability of the so-called improved split-step theta method for stochastic differential equations. First, we study the mean-square stability of the method for linear test equations with rea...We consider the mean-square stability of the so-called improved split-step theta method for stochastic differential equations. First, we study the mean-square stability of the method for linear test equations with real parameters. When 0 ≥ 3/2, the improved split-step theta methods can reproduce the mean-square stability of the linear test equations for any step sizes h 〉 0. Then, under a coupled condition on the drift and diffusion coefficients, we consider exponential mean-square stability of the method for nonlinear non-autonomous stochastic differential equations. Finally, the obtained results are supported by numerical experiments.展开更多
The study and modeling process of effervescent atomization are reviewed. The mechanism of droplet events and the treatment of liquid fragmentation process and dispersed particles are systematically presented, which in...The study and modeling process of effervescent atomization are reviewed. The mechanism of droplet events and the treatment of liquid fragmentation process and dispersed particles are systematically presented, which includes the primary atomization of Newtonian and non-Newtonian fluid, instability analysis, turbulence treatment, particle tracking, secondary atomization and droplets collision. The review on the sub-models involved in the simulation of effervescence is followed by a summary of the achievements of modeling. First is the validation of models; then the parametric study is summarized; the third part introduces the fitting formula of droplet mean size and impinging factors, and finally the scope of future study is indicated.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
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 thickness of a broken zone, a state parameter of roadway surrounding rock, is used as the index to evaluate the stabi1ity of surrounding rock of a deep roadway. The paper gives a theoretic formula for calculating the thickness of the broken zone. The author points out that not only the ultimate strength of rockmass but its residual strength and strain-softening level all have a great influence on the stability of surrounding rock of a deep roadway. The paper’s results show that to reinforce surrounding rock, raise its residual strength and lower its strain-softening level should be taken as a basic requirement for supports of a deep roadway. In addition, the research also indicates that it is impossible for roadway supports to change surrounding rock states of a deep roadway, so it is certain for them to work in a broken state. For this reason, a sufficient yieldable quantity is necessary for roadway supports used in deep mining.
基金supported by the National Natural Science Foundation of China (Grant No. 51079109)
文摘In the Xiaowan arch dam there are massive temperature cracks nearly parallel to the dam axis. Obviously, whether the cracks may spread or not during the water storage process is one of the crucial factors for the safety of a dam. In this paper, a new type of crack element, in which the contact component is implicitly included into the concrete component, is proposed to simulate the effects of the existing cracks. The crack element is proved by numerical example to share the merits of both conventional contact elements and joint elements. With a finite element model of the cracked arch dam together with its rock foundation established, the transient displacement and stress fields of the dam are obtained. The complicated rock foundation, the construction process of the arch dam, the massive cracks, the transient temperature field, as well as the water storage process have been taken into consideration in the simulation. In addition to the global model, several sub-models for typical crack tips are also generated with finer elements placed around the tips. Thus, more accurate displacement and stress distribution are obtained by simultaneous sub-model simulation. Based on the calculation of stress intensity factor for crack tips by extension method, the temperature cracks in the Xiaowan arch dam are finally proved to be stable.
基金supported by National Natural Science Foundation of China (Grant Nos. 91130003 and 11371157)the Scientific Research Innovation Team of the University “Aviation Industry Economy” (Grant No. 2016TD02)
文摘We consider the mean-square stability of the so-called improved split-step theta method for stochastic differential equations. First, we study the mean-square stability of the method for linear test equations with real parameters. When 0 ≥ 3/2, the improved split-step theta methods can reproduce the mean-square stability of the linear test equations for any step sizes h 〉 0. Then, under a coupled condition on the drift and diffusion coefficients, we consider exponential mean-square stability of the method for nonlinear non-autonomous stochastic differential equations. Finally, the obtained results are supported by numerical experiments.
基金supported by the National Natural Science Foundation of China (Grant Nos.11132008 and 11002136)
文摘The study and modeling process of effervescent atomization are reviewed. The mechanism of droplet events and the treatment of liquid fragmentation process and dispersed particles are systematically presented, which includes the primary atomization of Newtonian and non-Newtonian fluid, instability analysis, turbulence treatment, particle tracking, secondary atomization and droplets collision. The review on the sub-models involved in the simulation of effervescence is followed by a summary of the achievements of modeling. First is the validation of models; then the parametric study is summarized; the third part introduces the fitting formula of droplet mean size and impinging factors, and finally the scope of future study is indicated.
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.
