Under the' assumption of linearization of the free-surface condition, making use of Green's function method and the convolution theorem, analytic solutions of perturbation velocity potentials which correspond ...Under the' assumption of linearization of the free-surface condition, making use of Green's function method and the convolution theorem, analytic solutions of perturbation velocity potentials which correspond to three dimensional unsteady thickness problem and lifting problem caused respectively by arbitrary motions of a body and a hydrofoil beneath the water surface can be achieved in the closed form, In general, the whole perturbation velocity potential consists of three terms, namely φ=φ1+φ2+φ3 , where φ1 denotes the induced velocity potential of the surface singularity distribution in an unbounded fluid, φ2 denotes its mirror image and φ3 denotes that of wave formation which includes the memory effect of the action of the singularity distribution. Utilizing the polynomial expansion of sin[(t-τ)] , the similarity between φ2 and φ3 is discovered and thus a simpler differential relation between them is obtained. Applying this relation, the amount of work in calculation of φ3 which is the most time-consuming one will be reduced significantly. It is favorable not only for dealing with unsteady wave- making problems but also for solving the steady ones in virtue of evading a major difficulty which has to be encountered during the evaluation of an improper inte- gral containing a singularity in the Green's function. The limitation of this new technique turns out to be its slower convergence as the Froude number is lower.展开更多
A mathematical model for describing gas solid two phase steady mixed convection with phase change has been developed and numerical calculation methods presented.A melting liquid droplet failing a counter gas currenl e...A mathematical model for describing gas solid two phase steady mixed convection with phase change has been developed and numerical calculation methods presented.A melting liquid droplet failing a counter gas currenl expe- riences three processes,cooling of liquid droplet,solidification and cooling of the solid particle.The turbulent model used for Rayleigh number greater than 10~6 is a two equation(k—ε)model of turbulence.For phase change,an improved enthalpy method with varied time step is proposed.The gas particle two phase flow is described by using Eulerian-Lagrangian approach.Modified SIMPLE algorithm and Runge-Kutta method are used in interative calcu- lation.As an example of calculation,the flow in a special 2-dimensional axi-symmetrical prilling tower of diameter 20 m and height 50 m has been performed.Buoyancy effect is important for moving droplet with phase change. The model to be developed and analysis of results obtained in this paper are useful for engineering design in indus- try.展开更多
In the paper,we establish the existence of steady boundary layer solution of Boltzmann equation with specular boundary condition in Lx,v2∩Lx,v∞in half-space.The uniqueness,continuity and exponential decay of the sol...In the paper,we establish the existence of steady boundary layer solution of Boltzmann equation with specular boundary condition in Lx,v2∩Lx,v∞in half-space.The uniqueness,continuity and exponential decay of the solution are obtained,and such estimates are important to prove the Hilbert expansion of Boltzmann equation for half-space problem with specular boundary condition.展开更多
In this paper, we propose a non-autonomous convection-reaction diffusion system （CDI） with a nonlinear reaction source function. This model refers to the quantification and the distribution of antibiotic resistant b...In this paper, we propose a non-autonomous convection-reaction diffusion system （CDI） with a nonlinear reaction source function. This model refers to the quantification and the distribution of antibiotic resistant bacteria （ARB） in a river. The main contributions of this paper are： （i） the determination of the limit set of the system by applying the semigroups theory, it is shown that it is reduced to the solutions of the associated elliptic system （CDI）e, （ii） sufficient conditions for the existence of a positive solution of （CDI）e based on the Leray-Schauder＇s degree theory. Numerical simulations which support our theoretical analysis are also given.展开更多
文摘Under the' assumption of linearization of the free-surface condition, making use of Green's function method and the convolution theorem, analytic solutions of perturbation velocity potentials which correspond to three dimensional unsteady thickness problem and lifting problem caused respectively by arbitrary motions of a body and a hydrofoil beneath the water surface can be achieved in the closed form, In general, the whole perturbation velocity potential consists of three terms, namely φ=φ1+φ2+φ3 , where φ1 denotes the induced velocity potential of the surface singularity distribution in an unbounded fluid, φ2 denotes its mirror image and φ3 denotes that of wave formation which includes the memory effect of the action of the singularity distribution. Utilizing the polynomial expansion of sin[(t-τ)] , the similarity between φ2 and φ3 is discovered and thus a simpler differential relation between them is obtained. Applying this relation, the amount of work in calculation of φ3 which is the most time-consuming one will be reduced significantly. It is favorable not only for dealing with unsteady wave- making problems but also for solving the steady ones in virtue of evading a major difficulty which has to be encountered during the evaluation of an improper inte- gral containing a singularity in the Green's function. The limitation of this new technique turns out to be its slower convergence as the Froude number is lower.
文摘A mathematical model for describing gas solid two phase steady mixed convection with phase change has been developed and numerical calculation methods presented.A melting liquid droplet failing a counter gas currenl expe- riences three processes,cooling of liquid droplet,solidification and cooling of the solid particle.The turbulent model used for Rayleigh number greater than 10~6 is a two equation(k—ε)model of turbulence.For phase change,an improved enthalpy method with varied time step is proposed.The gas particle two phase flow is described by using Eulerian-Lagrangian approach.Modified SIMPLE algorithm and Runge-Kutta method are used in interative calcu- lation.As an example of calculation,the flow in a special 2-dimensional axi-symmetrical prilling tower of diameter 20 m and height 50 m has been performed.Buoyancy effect is important for moving droplet with phase change. The model to be developed and analysis of results obtained in this paper are useful for engineering design in indus- try.
基金supported by National Key R&D Program of China No.2021YFA1000800by the National Natural Science Foundation of China(Nos.12288201,12022114,12071439)。
文摘In the paper,we establish the existence of steady boundary layer solution of Boltzmann equation with specular boundary condition in Lx,v2∩Lx,v∞in half-space.The uniqueness,continuity and exponential decay of the solution are obtained,and such estimates are important to prove the Hilbert expansion of Boltzmann equation for half-space problem with specular boundary condition.
文摘In this paper, we propose a non-autonomous convection-reaction diffusion system （CDI） with a nonlinear reaction source function. This model refers to the quantification and the distribution of antibiotic resistant bacteria （ARB） in a river. The main contributions of this paper are： （i） the determination of the limit set of the system by applying the semigroups theory, it is shown that it is reduced to the solutions of the associated elliptic system （CDI）e, （ii） sufficient conditions for the existence of a positive solution of （CDI）e based on the Leray-Schauder＇s degree theory. Numerical simulations which support our theoretical analysis are also given.
