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EXPERIMENTAL AND NUMERICAL INVESTIGATION OF FREE SURFACE VORTEX

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Journal of Hydrodynamics 2008年第4期20卷 485-491页

作者： LI Hai-feng CHEN Hong-xun MA Zheng ZHOU Yi shanghai Institute of Applied Mathematics and mechanics Shanghai University Shanghai 200072 China china Ship Scientific Research Center Wuxi 214082 China

An experimental model was set up to investigate the formation and evolution of the free surface vortex. A Particle Image Velocimetry （PIV） was used to measure the free surface vortex flow field at different development stages. Flow visualization was used to locate the vortex position and find its structure. Empirical formulas about the critical submergence and the whole field structure were obtained. It is found that the tangential velocity distribution is similar to that of the Rankine vortex and the radial velocity changes little in the vortex functional scope. Vortex starts from the free surface and gradually intensifies to air entrainment vortex. The vortex core moves during the formation and evolution of the free surface vortex. Based on the experimental model, the vortex position and structure were predicted by numerical simulation combined with a vortex model and compared with that of the experiments, which shows satisfactory agreement.

关键词： free surface vortex Particle Image Velocimetry (PIV) numerical simulation rankine vortex

Steady-state responses of axially accelerating viscoelastic beams: Approximate analysis and numerical confirmation

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Science china(Physics,mechanics & Astronomy) 2008年第11期51卷 1707-1721页

作者： CHEN LiQun1,2 & DING Hu2 1 department of mechanics, shanghai university, shanghai 200444, china 2 shanghai Institute of Applied Mathematics and mechanics, shanghai 200070, china department of mechanics Shanghai University Shanghai China shanghai Institute of Applied Mathematics and mechanics Shanghai China

Nonlinear parametric vibration of axially accelerating viscoelastic beams is inves-tigated via an approximate analytical method with numerical confirmations. Based on nonlinear models of a finite-small-stretching slender beam moving at a speed with a periodic fluctuation, a solvability condition is established via the method of multiple scales for subharmonic resonance. Therefore, the amplitudes of steady-state periodic responses and their existence conditions are derived. The amplitudes of stable steady-state responses increase with the amplitude of the axial speed fluctuation, and decrease with the viscosity coefficient and the nonlinear coefficient. The minimum of the detuning parameter which causes the existence of a stable steady-state periodic response decreases with the amplitude of the axial speed fluctuation, and increases with the viscosity coefficient. Nu-merical solutions are sought via the finite difference scheme for a nonlinear par-tial-differential equation and a nonlinear integro-partial-differential equation. The calculation results qualitatively confirm the effects of the related parameters pre-dicted by the approximate analysis on the amplitude and the existence condition of the stable steady-state periodic responses. Quantitative comparisons demonstrate that the approximate analysis results have rather high precision.

关键词： nonlinearity parametric vibration axially accelerating beam method of multiple scales numerical confir-mation

GURTIN VARIATIONAL PRINCIPLE AND FINITE ELEMENT SIMULATION FOR DYNAMICAL PROBLEMS OF FLUID-SATURATED POROUS MEDIA

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Acta Mechanica Solida Sinica 2003年第1期16卷 24-32页

作者： Yang Xiao Cheng Changjun department o,f mechanics, shanghai Institute of Applied Mathematics and mechanics,shanghai university,shanghai 200436,china) department of mechanics Shanghai Inst. of Appl. Math./Mech. Shanghai University Shanghai 200436 China

Based on the theory of porous media, a general Gurtin variational principle for the initial boundary value problem of dynamical response of fluid-saturated elastic porous media is developed by assuming infinitesimal deformation and incompressible constituents of the solid and fluid phase. The finite element formulation based on this variational principle is also derived. As the functional of the variational principle is a spatial integral of the convolution formulation, the general finite element discretization in space results in symmetrical differential-integral equations in the time domain. In some situations, the differential-integral equations can be reduced to symmetrical differential equations and, as a numerical example, it is employed to analyze the reflection of one-dimensional longitudinal wave in a fluid-saturated porous solid. The numerical results can provide further understanding of the wave propagation in porous media.

关键词： saturated porous media Gurtin variational principle finite element method longitudinal wave

FORMATION AND INFLUENCING FACTORS OF FREE SURFACE VORTEX IN A BARREL WITH A CENTRAL ORIFICE AT BOTTOM

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Journal of Hydrodynamics 2009年第2期21卷 238-244页

Based on the Navier-Stokes equations with considering the effect of the Coriolis force, the finite volume method was employed to discretize the governing equations, the SIMPLE method was adopted to solve the discretized equations, and the flow field in a barrel with an outlet at the center of the bottom was simulated. The numerical results agree well with the experimental data. From the Lagrangian, the relations among the acceleration, the Coriolis force and the viscosity force were analyzed. The results show that the Coriolis force is the major factor that causes the formation of the vortex. The flow fields in the flume under different incoming flow conditions were numerically simulated using the software Fluent. The numerical simulations show good agreement with the experiments for the shape and position of the vortex.

关键词： free surface vortex Coriolis force numerical simulation

TURBULENT MIXING AND EVOLUTION IN A STABLY STRATIFIED FLOW WITH A TEMPERATURE STEP

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Journal of Hydrodynamics 2009年第1期21卷 84-92页

作者： QIU Xiang ZHANG Dao-xiang LU Zhi-ming LIU Yu-lu shanghai Institute of Applied Mathematics and mechanics Shanghai University Shanghai 200072 China department of Mathematics Shanghai University Shanghai 200444 China

Large-Eddy Simulation （LES） is applied to examine the turbulent mixing and evolution in a stably stratified flow with a thermally sharp interface. Turbulent velocity intensities and turbulent kinetic energy are analyzed by considering the mean shear and stratification effects. The evolution of turbulent mixing layer and turbulent structures are mainly investigated. The results show that the streamwise intensities are much larger than the vertical intensities, and vertical fluctuations decay more rapidly at the presence of stratification. The qualitatively computational results suggest that the mixing layer, defined by the mean temperature, inclines to the side with small inlet velocity. The evolution of the half-width of the mixing layer shows two different slopes. The turbulent structure with high vorticity is restricted in the mixing layer especially in strong stratified cases.

关键词： stratified turbulence turbulent mixing turbulent structure Large-Eddy Simulation (LES)

A NEW CONTINUUM TRAFFIC MODEL WITH THE EFFECT OF VISCOSITY

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Journal of Hydrodynamics 2011年第2期23卷 164-169页

作者： SONG Tao LI Xing-li KUANG Hua DONG Li-yun shanghai Institute of Applied Mathematics and mechanics Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University Shanghai 200072 China School of Applied Science Taiyuan University of Science and Technology Taiyuan 030024 China College of Physics and Technology Guangxi Normal University Guilin 541004 China

Through considering the connection between microscopic car-following model and macroscopic continuum model, a new viscous vehicular flow model is proposed, in which the viscosity coefficient is determined by a more realistic constitutive relationship between averaged reaction time of drivers and the car density. Further analysis indicates that two traffic sound speeds in this viscous model may determine the existence and the stability of traveling wave solutions with an analytical method.

关键词： viscosity continuum traffic model reaction time traffic sound speed traveling wave

CURVILINEAR PATHS AND TRUST REGION METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR UNCONSTRAINED OPTIMIZATION

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Journal of Computational Mathematics 2001年第3期19卷 241-258页

作者： De-tong Zhu (department of Mathematics, shanghai Normal university, shanghai 200234, china) 上海师范大学上海 200234

Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments.

关键词： curvilinear paths trust region methods nonmonotonic technique unconstrained optimization

The Geometric Structure of Strange Attractors in the Lozi Map

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Communications in Nonlinear Science and Numerical Simulation 1998年第2期3卷 67-71页

作者： Yongluo CAO and Zengrong LIU* (department of Mathematics, Suzhou university,Suzhou 215006, china) *(department of Mathematics, shanghai university,shanghai 200072, china) (E mail: ***) department of Mathematics Suzhou University Suzhou 215006 China department of Mathematics Shanghai University Shanghai 200072 China

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关键词： strange attractor transversal homoclinic point weak transversal homoclinic point

DISSIPATIVITY AND EXPONENTIAL STABILITY OF θ-METHODS FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED LAG

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Journal of Computational Mathematics 2003年第6期21卷 715-726页

作者： Hong-jiong Tian (department of Mathematics, shanghai Normal university, shanghai 200234, china) department of Mathematics Shanghai Normal University 上海 200234

This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1.

关键词： Singular perturbation θ-methods Dissipativity Exponential stability.