It is known that the Boltzmann equation has close relation to the classical systems in fluid dynamics. However, it provides more information on the microscopic level so that some phenomena, like the thermal creep flow...It is known that the Boltzmann equation has close relation to the classical systems in fluid dynamics. However, it provides more information on the microscopic level so that some phenomena, like the thermal creep flow, can not be modeled by the classical systems of fluid dynamics, such as the Euler equations. The author gives an example to show this phenomenon rigorously in a special setting. This paper is completely based on the author's recent work, jointly with Wang and Yang.展开更多
The usual heat flow moves along the direction from high temperature place to the low one,as often observed in the daily life.However,when the gas is very rarefied,the gas may move along a different way,that is,the so-...The usual heat flow moves along the direction from high temperature place to the low one,as often observed in the daily life.However,when the gas is very rarefied,the gas may move along a different way,that is,the so-called thermal creep flow moves along the direction from the low temperature place to the high one.In this note,we will survey our recent mathematical works on this topic,mainly based on[27]and[25].展开更多
We present numerical simulations of a new system of micro-pump based on the thermal creep effect described by the kinetic theory of gases.This device is made of a simple smooth and curved channel with a periodic tempe...We present numerical simulations of a new system of micro-pump based on the thermal creep effect described by the kinetic theory of gases.This device is made of a simple smooth and curved channel with a periodic temperature distribution.Using the Boltzmann-BGK model as the governing equation for the gas flow,we develop a numerical method based on a deterministic finite volume scheme,implicit in time,with an implicit treatment of the boundary conditions.This method is comparatively less sensitive to the slow flow velocity than the usual Direct Simulation Monte Carlo method in case of long devices,and turns out to be accurate enough to compute macroscopic quantities like the pressure field in the channel.Our simulations show the ability of the device to produce a one-way flow that has a pumping effect.展开更多
Due to the rapid advances inmicro-electro-mechanical systems(MEMS),the study of microflows becomes increasingly important.Currently,the molecular-based simulation techniques are the most reliable methods for rarefied ...Due to the rapid advances inmicro-electro-mechanical systems(MEMS),the study of microflows becomes increasingly important.Currently,the molecular-based simulation techniques are the most reliable methods for rarefied flow computation,even though these methods face statistical scattering problem in the low speed limit.With discretized particle velocity space,a unified gas-kinetic scheme(UGKS)for entire Knudsen number flow has been constructed recently for flow computation.Contrary to the particle-based direct simulation Monte Carlo(DSMC)method,the unified scheme is a partial differential equation-based modeling method,where the statistical noise is totally removed.But,the common point between the DSMC and UGKS is that both methods are constructed through direct modeling in the discretized space.Due to the multiscale modeling in the unified method,i.e.,the update of both macroscopic flow variables and microscopic gas distribution function,the conventional constraint of time step being less than the particle collision time inmany direct Boltzmann solvers is released here.The numerical tests show that the unified scheme is more efficient than the particle-basedmethods in the low speed rarefied flow computation.Themain purpose of the current study is to validate the accuracy of the unified scheme in the capturing of non-equilibrium flow phenomena.In the continuum and free molecular limits,the gas distribution function used in the unified scheme for the flux evaluation at a cell interface goes to the corresponding Navier-Stokes and free molecular solutions.In the transition regime,the DSMC solution will be used for the validation of UGKS results.This study shows that the unified scheme is indeed a reliable and accurate flow solver for low speed non-equilibrium flows.It not only recovers the DSMC results whenever available,but also provides high resolution results in cases where the DSMC can hardly afford the computational cost.In thermal creep flow simulation,surprising solution,such as the gas flowing from hot to cold regions along the wall surface,is observed for the first time by the unified scheme,which is confirmed later through intensive DSMC computation.展开更多
文摘It is known that the Boltzmann equation has close relation to the classical systems in fluid dynamics. However, it provides more information on the microscopic level so that some phenomena, like the thermal creep flow, can not be modeled by the classical systems of fluid dynamics, such as the Euler equations. The author gives an example to show this phenomenon rigorously in a special setting. This paper is completely based on the author's recent work, jointly with Wang and Yang.
文摘The usual heat flow moves along the direction from high temperature place to the low one,as often observed in the daily life.However,when the gas is very rarefied,the gas may move along a different way,that is,the so-called thermal creep flow moves along the direction from the low temperature place to the high one.In this note,we will survey our recent mathematical works on this topic,mainly based on[27]and[25].
基金This research was supported partially by“Projet International de Cooperation Scientifique(PICS)”of CNRS(Grant No.3195)by grants-in-aid for scientific research from JSPS(Nos.17656033 and 20360046).
文摘We present numerical simulations of a new system of micro-pump based on the thermal creep effect described by the kinetic theory of gases.This device is made of a simple smooth and curved channel with a periodic temperature distribution.Using the Boltzmann-BGK model as the governing equation for the gas flow,we develop a numerical method based on a deterministic finite volume scheme,implicit in time,with an implicit treatment of the boundary conditions.This method is comparatively less sensitive to the slow flow velocity than the usual Direct Simulation Monte Carlo method in case of long devices,and turns out to be accurate enough to compute macroscopic quantities like the pressure field in the channel.Our simulations show the ability of the device to produce a one-way flow that has a pumping effect.
基金Hong Kong Research Grant Council(621709,621011)and grants SRFI11SC05 and RPC10SC11 atHKUST.J.C.Huang was supported by National Science Council of Taiwan through grant No.NSC 100-2221-E-019-048-MY3.
文摘Due to the rapid advances inmicro-electro-mechanical systems(MEMS),the study of microflows becomes increasingly important.Currently,the molecular-based simulation techniques are the most reliable methods for rarefied flow computation,even though these methods face statistical scattering problem in the low speed limit.With discretized particle velocity space,a unified gas-kinetic scheme(UGKS)for entire Knudsen number flow has been constructed recently for flow computation.Contrary to the particle-based direct simulation Monte Carlo(DSMC)method,the unified scheme is a partial differential equation-based modeling method,where the statistical noise is totally removed.But,the common point between the DSMC and UGKS is that both methods are constructed through direct modeling in the discretized space.Due to the multiscale modeling in the unified method,i.e.,the update of both macroscopic flow variables and microscopic gas distribution function,the conventional constraint of time step being less than the particle collision time inmany direct Boltzmann solvers is released here.The numerical tests show that the unified scheme is more efficient than the particle-basedmethods in the low speed rarefied flow computation.Themain purpose of the current study is to validate the accuracy of the unified scheme in the capturing of non-equilibrium flow phenomena.In the continuum and free molecular limits,the gas distribution function used in the unified scheme for the flux evaluation at a cell interface goes to the corresponding Navier-Stokes and free molecular solutions.In the transition regime,the DSMC solution will be used for the validation of UGKS results.This study shows that the unified scheme is indeed a reliable and accurate flow solver for low speed non-equilibrium flows.It not only recovers the DSMC results whenever available,but also provides high resolution results in cases where the DSMC can hardly afford the computational cost.In thermal creep flow simulation,surprising solution,such as the gas flowing from hot to cold regions along the wall surface,is observed for the first time by the unified scheme,which is confirmed later through intensive DSMC computation.