We investigate the symmetry reduction for the two-dimensional incompressible Navier-Stokes equationin conventional stream function form through Lie symmetry method and construct some similarity reduction solutions.Two...We investigate the symmetry reduction for the two-dimensional incompressible Navier-Stokes equationin conventional stream function form through Lie symmetry method and construct some similarity reduction solutions.Two special cases in [D.K.Ludlow,P.A.Clarkson,and A.P.Bassom,Stud.Appl.Math.103 (1999) 183] and a theoremin [S.Y.Lou,M.Jia,X.Y.Tang,and F.Huang,Phys.Rev.E 75 (2007) 056318] are retrieved.展开更多
By applying bromide ion as tracer, the channeling flow has been quantitatively described in saline rice soil and alkaline soil of Da＇an City, Jilin Province of China. Breakthrough curves of bromide ion in the saline ...By applying bromide ion as tracer, the channeling flow has been quantitatively described in saline rice soil and alkaline soil of Da＇an City, Jilin Province of China. Breakthrough curves of bromide ion in the saline rice soils after 1-year cultivation and 5-year cultivation and alkaline soil have been attained. Results show that the rice cultivation practice can improve the alkaline soil structure, however, it can accelerate the development of channeling flow pathway. Therefore, the channeling flow pathway has been developed widely in saline rice soil, but rarely in the alkaline soil. Three models of convection-dispersion equation （CDE）, transfer functional model （TFM） and Back-Progation Network （BP Network） were used to simulate the transportation process of bromide ion. The peaks of probability density function of saline rice soil are higher with left skewed feature compared with that of the alkaline soil. It shows that the TIM and CDE can simulate the transportation process of the bromide ion in saline rice soil after 5-year cultivation, however, some deviation exists when it was used to simulate transportation process of bromide ion in saline rice soil after 1-year cultivation and alkaline soil; BP network can effectively simulate transportation process of bromide ion in both saline rice soil and alkaline soil.展开更多
Heat transfer and hydrodynamics of two phase closed thermosyphon （TPCT） is studied using finite difference method of Stream function and vorticity. The mathematical model is formed for both vapor phase and liquid fi...Heat transfer and hydrodynamics of two phase closed thermosyphon （TPCT） is studied using finite difference method of Stream function and vorticity. The mathematical model is formed for both vapor phase and liquid film in a non-dimensional form. The momentum and energy equations as parabolic equations have been solved by means of the locally one-dimensional scheme of A.A. Samarskii. The Poisson equation for the stream function has been approximated on the basis of the discrete scheme ＂cross＂. The obtained system of algebraic equations has been solved by the successive over relaxation method. The effect of the Rayleigh number on the velocity and temperature fields in the domain of interest and on the average Nusselt number at the solid-fluid interfaces is investigated. It was found that increase in the Rayleigh number leads to the increment of both the average Nusselt number and the stream function in the vapor zone.展开更多
The flow of a freely falling liquid film of low Reynolds number down a vertical long periodic sine-shaped wavy plate of small corrugations is researched theoretically. A model based on perturbation method and power se...The flow of a freely falling liquid film of low Reynolds number down a vertical long periodic sine-shaped wavy plate of small corrugations is researched theoretically. A model based on perturbation method and power series is presented. A stream function is introduced into the governing equations and two sets of equations describing the film flow separately at zeroth and first order are developed. The zeroth order equation is solved directly. The first order equations is solved at the leading approximation. Effect of parameters Re, M, λ and ε on the free surface wave of film is discussed.展开更多
In this article the approach was used to coherent assessment based on the intensity of air pollution sources impact on the impurity concentration at a few fixed points to monitor air quality. The numerical analogue ...In this article the approach was used to coherent assessment based on the intensity of air pollution sources impact on the impurity concentration at a few fixed points to monitor air quality. The numerical analogue of Duhamers theorem was used to describe processes of propagation of impurity in the atmosphere. Such approach allows you to count on essential increase of calculation accuracy based on mathematical models of reasonable complexity. The inverse problem of pollutants propagation in the atmosphere based on the measurements of the impurity concentration in stationary or mobile control points was solved by the sequential function approximation The solution was presented in the form of a digital filter.展开更多
The aim of this study was to assess the runoff amount from a catchment characterized by diverse land uses by using the Soil Conservation Service Curve Number(SCS-CN) method based on Curve Number(CN) defined for domina...The aim of this study was to assess the runoff amount from a catchment characterized by diverse land uses by using the Soil Conservation Service Curve Number(SCS-CN) method based on Curve Number(CN) defined for dominant homogeneous elementary sub-regions.The calculations employed the SCS-CN method,involving the division of the catchment in two homogeneous parts and determining the runoff amount.The obtained results were compared with the results provided by three other CN determination methods,i.e.the Hawkins function,the kinetics equation,and a complementary error function peak.The catchment is located in a mountain dominated by forest land cover.Empirical CN-Precipitation(CN_(emp)-P) data pairs were analyzed using the mentioned methods,and the highest quality score was achieved from model 1.The results suggest that dividing a catchment into two homogeneous areas and determining their separate CN parameters,used later on to calculate the runoff by means of the presented approach,could be an alternative to the standard methods.The described method is relatively easy,and as it does not require an adoption of numerous parameters,and it can be employed for designing hydraulic facilities.展开更多
In this paper, Crouzeix-Raveart type nonconforming rectangular element is applied to the Mumford-Shah functional for image segmentation subjected to Robin boundary conditions. Meanwhile, by using the special orthogona...In this paper, Crouzeix-Raveart type nonconforming rectangular element is applied to the Mumford-Shah functional for image segmentation subjected to Robin boundary conditions. Meanwhile, by using the special orthogonality of this element＇s basic functions, the convergence analysis for L2-norm and broken H1-norm with semi-implicit scheme is presented. And the error order is improved to the optimal, too.展开更多
It is well-known that every member of the KdV hierarchy of equations can be obtained from the AKNS hierarchy of equations by imposing a simple reduction. The author finds that the reduction conditions of the potential...It is well-known that every member of the KdV hierarchy of equations can be obtained from the AKNS hierarchy of equations by imposing a simple reduction. The author finds that the reduction conditions of the potentials in the spectral problem can be replaced by adding additional eigenfunction equations to the spectral problem, and then shows that the restricted KdV flows, such as the Neumann system, the Gamier system and the generalized multicomponent Henon-Hieles system, are a kind of special reductions of the restricted AKNS flows.展开更多
This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity dis...This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity distribution function obtained by the DSMC method converges to a modified form of the Boltzmann equation,which is the equation of the gas-kinetic unified algorithm to directly solve the molecular velocity distribution function.Their convergence is derived through mathematical treatment.The collision frequency is presented using various molecular models and the local equilibrium distribution function is obtained by Enskog expansion using the converged equation of the DSMC method.These two expressions agree with those used in the unified algorithm.Numerical validation of the converging consistency between these two approaches is illustrated by simulating the pressure driven Poiseuille flow in the slip transition flow regime and the two-dimensional and three-dimensional flows around a circular cylinder and spherical-cone reentry body covering the whole flow regimes from low speed micro-channel flow to high speed non-equilibrium aerothermodynamics.展开更多
A new(γA,σB)-matrix KP hierarchy with two time series γA and σB,which consists of γA-flow,σB-flow and mixed γA and σB-evolution equations of eigenfunctions,is proposed.The reduction and constrained flows of(...A new(γA,σB)-matrix KP hierarchy with two time series γA and σB,which consists of γA-flow,σB-flow and mixed γA and σB-evolution equations of eigenfunctions,is proposed.The reduction and constrained flows of(γA,σB)matrix KP hierarchy are studied.The dressing method is generalized to the(γA,σB)-matrix KP hierarchy and some solutions are presented.展开更多
基金Supported by National Natural Science Foundations of China under Grant Nos.10735030,10475055,10675065,and 90503006National Basic Research Program of China (973 Program) under Grant No.2007CB814800+2 种基金PCSIRT (IRT0734)the Research Fund of Postdoctoral of China under Grant No.20070410727Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20070248120
文摘We investigate the symmetry reduction for the two-dimensional incompressible Navier-Stokes equationin conventional stream function form through Lie symmetry method and construct some similarity reduction solutions.Two special cases in [D.K.Ludlow,P.A.Clarkson,and A.P.Bassom,Stud.Appl.Math.103 (1999) 183] and a theoremin [S.Y.Lou,M.Jia,X.Y.Tang,and F.Huang,Phys.Rev.E 75 (2007) 056318] are retrieved.
基金Under the auspices of the Key Innovation Project of Chinese Academy of Sciences (No. KZCX1-SW-19-02)
文摘By applying bromide ion as tracer, the channeling flow has been quantitatively described in saline rice soil and alkaline soil of Da＇an City, Jilin Province of China. Breakthrough curves of bromide ion in the saline rice soils after 1-year cultivation and 5-year cultivation and alkaline soil have been attained. Results show that the rice cultivation practice can improve the alkaline soil structure, however, it can accelerate the development of channeling flow pathway. Therefore, the channeling flow pathway has been developed widely in saline rice soil, but rarely in the alkaline soil. Three models of convection-dispersion equation （CDE）, transfer functional model （TFM） and Back-Progation Network （BP Network） were used to simulate the transportation process of bromide ion. The peaks of probability density function of saline rice soil are higher with left skewed feature compared with that of the alkaline soil. It shows that the TIM and CDE can simulate the transportation process of the bromide ion in saline rice soil after 5-year cultivation, however, some deviation exists when it was used to simulate transportation process of bromide ion in saline rice soil after 1-year cultivation and alkaline soil; BP network can effectively simulate transportation process of bromide ion in both saline rice soil and alkaline soil.
文摘Heat transfer and hydrodynamics of two phase closed thermosyphon （TPCT） is studied using finite difference method of Stream function and vorticity. The mathematical model is formed for both vapor phase and liquid film in a non-dimensional form. The momentum and energy equations as parabolic equations have been solved by means of the locally one-dimensional scheme of A.A. Samarskii. The Poisson equation for the stream function has been approximated on the basis of the discrete scheme ＂cross＂. The obtained system of algebraic equations has been solved by the successive over relaxation method. The effect of the Rayleigh number on the velocity and temperature fields in the domain of interest and on the average Nusselt number at the solid-fluid interfaces is investigated. It was found that increase in the Rayleigh number leads to the increment of both the average Nusselt number and the stream function in the vapor zone.
基金Acknowledgement： This work is supported by Natural Science Foundation of Tianjin of China （No. 07JCYBJC01300）.
文摘The flow of a freely falling liquid film of low Reynolds number down a vertical long periodic sine-shaped wavy plate of small corrugations is researched theoretically. A model based on perturbation method and power series is presented. A stream function is introduced into the governing equations and two sets of equations describing the film flow separately at zeroth and first order are developed. The zeroth order equation is solved directly. The first order equations is solved at the leading approximation. Effect of parameters Re, M, λ and ε on the free surface wave of film is discussed.
文摘In this article the approach was used to coherent assessment based on the intensity of air pollution sources impact on the impurity concentration at a few fixed points to monitor air quality. The numerical analogue of Duhamers theorem was used to describe processes of propagation of impurity in the atmosphere. Such approach allows you to count on essential increase of calculation accuracy based on mathematical models of reasonable complexity. The inverse problem of pollutants propagation in the atmosphere based on the measurements of the impurity concentration in stationary or mobile control points was solved by the sequential function approximation The solution was presented in the form of a digital filter.
基金Dean of the Faculty of Environmental Engineering and Land Surveying, University of Agriculture in Krakow, for financial support
文摘The aim of this study was to assess the runoff amount from a catchment characterized by diverse land uses by using the Soil Conservation Service Curve Number(SCS-CN) method based on Curve Number(CN) defined for dominant homogeneous elementary sub-regions.The calculations employed the SCS-CN method,involving the division of the catchment in two homogeneous parts and determining the runoff amount.The obtained results were compared with the results provided by three other CN determination methods,i.e.the Hawkins function,the kinetics equation,and a complementary error function peak.The catchment is located in a mountain dominated by forest land cover.Empirical CN-Precipitation(CN_(emp)-P) data pairs were analyzed using the mentioned methods,and the highest quality score was achieved from model 1.The results suggest that dividing a catchment into two homogeneous areas and determining their separate CN parameters,used later on to calculate the runoff by means of the presented approach,could be an alternative to the standard methods.The described method is relatively easy,and as it does not require an adoption of numerous parameters,and it can be employed for designing hydraulic facilities.
文摘In this paper, Crouzeix-Raveart type nonconforming rectangular element is applied to the Mumford-Shah functional for image segmentation subjected to Robin boundary conditions. Meanwhile, by using the special orthogonality of this element＇s basic functions, the convergence analysis for L2-norm and broken H1-norm with semi-implicit scheme is presented. And the error order is improved to the optimal, too.
基金Project supported by the National Natural Science Foundation of China (No.10871165)
文摘It is well-known that every member of the KdV hierarchy of equations can be obtained from the AKNS hierarchy of equations by imposing a simple reduction. The author finds that the reduction conditions of the potentials in the spectral problem can be replaced by adding additional eigenfunction equations to the spectral problem, and then shows that the restricted KdV flows, such as the Neumann system, the Gamier system and the generalized multicomponent Henon-Hieles system, are a kind of special reductions of the restricted AKNS flows.
基金supported by the National Natural Science Foundation of China (Grant Nos. 91016027 and 91130018)
文摘This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity distribution function obtained by the DSMC method converges to a modified form of the Boltzmann equation,which is the equation of the gas-kinetic unified algorithm to directly solve the molecular velocity distribution function.Their convergence is derived through mathematical treatment.The collision frequency is presented using various molecular models and the local equilibrium distribution function is obtained by Enskog expansion using the converged equation of the DSMC method.These two expressions agree with those used in the unified algorithm.Numerical validation of the converging consistency between these two approaches is illustrated by simulating the pressure driven Poiseuille flow in the slip transition flow regime and the two-dimensional and three-dimensional flows around a circular cylinder and spherical-cone reentry body covering the whole flow regimes from low speed micro-channel flow to high speed non-equilibrium aerothermodynamics.
基金Supported by the National Science Foundation of China under Grant Nos. 10801083,10901090,11171175China Postdoctoral Science Funded Project (20110490408)Chinese Universities Scientific Fund under Grant No. 2011JS041
文摘A new(γA,σB)-matrix KP hierarchy with two time series γA and σB,which consists of γA-flow,σB-flow and mixed γA and σB-evolution equations of eigenfunctions,is proposed.The reduction and constrained flows of(γA,σB)matrix KP hierarchy are studied.The dressing method is generalized to the(γA,σB)-matrix KP hierarchy and some solutions are presented.
