Adaptive Moving Mesh Central-Upwind Schemes for Hyperbolic System of PDEs:Applications to Compressible Euler Equations and Granular Hydrodynamics

We introduce adaptive moving mesh central-upwind schemes for one-and two-dimensional hyperbolic systems of conservation and balance laws.The proposed methods consist of three steps.First,the solution is evolved by solving the studied system by the second-order semi-discrete central-upwind scheme on either the one-dimensional nonuniform grid or the two-dimensional structured quadrilateral mesh.When the evolution step is complete,the grid points are redistributed according to the moving mesh differential equation.Finally,the evolved solution is projected onto the new mesh in a conservative manner.The resulting adaptive moving mesh methods are applied to the one-and two-dimensional Euler equations of gas dynamics and granular hydrodynamics systems.Our numerical results demonstrate that in both cases,the adaptive moving mesh central-upwind schemes outperform their uniform mesh counterparts.

LOGARITHMICALLY IMPROVED REGULARITY CRITERION FOR THE 3D GENERALIZED MAGNETO-HYDRODYNAMIC EQUATIONS

This article proves the logarithmically improved Serrin＇s criterion for solutions of the 3D generalized magneto-hydrodynamic equations in terms of the gradient of the velocity field, which can be regarded as improvement of results in [10] （Luo Y W. On the regularity of generalized MHD equations. J Math Anal Appl, 2010, 365： 806-808） and [18] （Zhang Z J. Remarks on the regularity criteria for generalized MHD equations. J Math Anal Appl, 2011, 375：799 802）.

Monolithic Coupling of the Pressure and Rigid Body Motion Equations in Computational Marine Hydrodynamics

In Fluid Structure Interaction(FSI) problems encountered in marine hydrodynamics, the pressure field and the velocity of the rigid body are tightly coupled. This coupling is traditionally resolved in a partitioned manner by solving the rigid body motion equations once per nonlinear correction loop, updating the position of the body and solving the fluid flow equations in the new configuration. The partitioned approach requires a large number of nonlinear iteration loops per time–step. In order to enhance the coupling, a monolithic approach is proposed in Finite Volume(FV) framework,where the pressure equation and the rigid body motion equations are solved in a single linear system. The coupling is resolved by solving the rigid body motion equations once per linear solver iteration of the pressure equation, where updated pressure field is used to calculate new forces acting on the body, and by introducing the updated rigid body boundary velocity in to the pressure equation. In this paper the monolithic coupling is validated on a simple 2D heave decay case. Additionally, the method is compared to the traditional partitioned approach(i.e. "strongly coupled" approach) in terms of computational efficiency and accuracy. The comparison is performed on a seakeeping case in regular head waves, and it shows that the monolithic approach achieves similar accuracy with fewer nonlinear correctors per time–step. Hence, significant savings in computational time can be achieved while retaining the same level of accuracy.

GLOBAL WEAK SOLUTIONS TO ONE-DIMENSIONAL COMPRESSIBLE VISCOUS HYDRODYNAMIC EQUATIONS

In this article, we are concerned with the global weak solutions to the 1D com- pressible viscous hydrodynamic equations with dispersion correction δ2ρ（（φ（ρ））xxφ′（ρ））x with φ（ρ） = ρα. The model consists of viscous stabilizations because of quantum Fokker-Planck operator in the Wigner equation and is supplemented with periodic boundary and initial con- ditions. The diffusion term εuxx in the momentum equation may be interpreted as a classical conservative friction term because of particle interactions. We extend the existence result in [1] （α=1/2） to 0 〈 α ≤ 1. In addition, we perform the limit ε→0 with respect to 0 〈 α ≤1/2.

An alternating direction implicit （ADI） numerical model for two－dimensional hydrodynamic equations

A two-dimensional computational model is develope for the calulation of tides, storm surges and otherlong-period waves in coastal and shelf waters. The Partial differental equations are approximated by two sets of difference equations on a space-staggered grid system. Both sets are explicit with one set for water level and x-component velocity, and another for water level and y-component velocity. These two sets are used successively for stepby-step solution in time. An analytical investigation on the linearized sets of the difference equations indicates that thecomputational scheme is unconditionally stable. The model is of second order accuracy both in space and in time andconserves mass and momentum. Simulations of surface elevation caused by periodic forcing in one-opening rectangularbasin with flat topography and by steady wind stress in the basin with flat or slope topography show that the computed results are in excellent agreement with the corresponding analytic solutions. The steady-tate wind-induced setupin a ofed basin with discontinuous topography computed with the present model are also in excellent agreement withthe results from Leendertse's model. Finally, the model is applied to hindcast a storm surge in the South China Seaand reproduces the surge elevation satisfactorily.

The Third Invariant Form of Hydrodynamic Equations and Application for Definition of Water Hammer Characteristics in Pipe

There were for a long time two invariant forms of hydrodynamic equations： one was related to coordinate system of references, and the other was versus to measure units of characteristics. These both invariant forms had important roles in the development of theoretical and practical applications of hydro-aerodynamics and related industries. The third invariant form of hydrodynamic equations is one for the dimensions of spaces. For this goal, the hyper quantities （space and physics） are introduced. Then these are created we can easily cover all problems in arbitrary dimensions （3D, 2D, 1D, separate space for liquids or constituent matters）. In particularly, when they are applied to water hammer problem, which is an especially problem, we can receive immediately celerity and pressure of the event.

Normalization of Hydrodynamic Coefficients in Morison Equation

The hydrodynamic coefficients C-d and C-m are not only dependent on the size of slender cylinder, its location in water, KC number and Re number, but also vary with environmental conditions, i.e., in regular waves or in irregular waves, in pure waves or in wave-current coexisting field. In this paper, the normalization of hydrodynamic coefficients for various environmental conditions is discussed. When a proper definition of KC number and proper characteristic values of irregular waves are used, a unified relationship between C-d, C-m and KC number for regular waves, irregular waves, pure waves and wave-current coexisting field can be obtained.

三维Electro-Hydrodynamics方程组光滑解的延拓准则

研究了三维Electro-Hydrodynamics方程组局部光滑解的延拓准则,利用负指标Besov空间中的对数Sobolev不等式和Kato-Ponce交换子估计方法,在Besov空间中获得了只涉及速度场水平分量的最优延拓准则,改进和推广了已有关于Electro-Hydrodynamics方程组正则性准则的部分结论,是Electro-Hydrodynamics方程组正则性理论的有益补充。

ON THE ENERGY EQUATION FOR A SPATIALLY DEVELOPING INSTABILITY WAVE IN THE THEORY OF HYDRODYNAMIC STABILITY

In this article,it is shown that the energy equation for a spatially developing disturbance used in all the literatures dealing with the problem of hydrodynamic stability suffers from a small,but crucial error.

General solution of the modified Korteweg-de-Vries equation in the lattice hydrodynamic model

Traffic congestion is related to various density waves, which might be described by the nonlinear wave equations, such as the Burgers, Korteweg-de-Vries （KdV） and modified Korteweg-de-Vries （mKdV） equations. In this paper, the mKdV equations of four different versions of lattice hydrodynamic models, which describe the kink-antikink soliton waves are derived by nonlinear analysis. Furthermore, the general solution is given, which is applied to solving a new model -- the lattice hydrodynamic model with bidirectional pedestrian flow. The result shows that this general solution is consistent with that given by previous work.

Time-dependent Ginzburg-Landau equation for lattice hydrodynamic model describing pedestrian flow

A thermodynamic theory is formulated to describe the phase transition and critical phenomena in pedestrian flow. Based on the extended lattice hydrodynamic pedestrian model taking the interaction of the next-nearest-neighbor persons into account, the time-dependent Ginzburg-Landau （TDGL） equation is derived to describe the pedestrian flow near the critical point through the nonlinear analysis method. The corresponding two solutions, the uniform and the kink solutions, are given. The coexisting curve, spinodal line, and critical point are obtained by the first and second derivatives of the thermodynamic potential.

Numerical Method for Solving Relativistic Hydrodynamic Equation Including Quark-Fragment Effect

In this paper, a numerical method is given to solve relativistic hydrodynamic equations with source terms by conservative finite difference scheme. In calculation, QGP (quark gluon plasma) phase transition is also considered. The numerical experiments have verified the effectiveness of the numerical method and some computational results are illustrated.

Hydrodynamic Lubrication of Elastic Foil Gas Bearing Using Over Relaxation Iteration Method and Non-Dimensional Equation

The purpose is to accurately predict the performance of foil bearing and achieve accurate results in the design of foil bearing structure.A new type of foil bearing with surface microstructure is used as experimental material.First,the lubrication mechanism of elastic foil gas bearing is analyzed.Then,the numerical solution process of the static bearing capacity and friction torque is analyzed,including the discretization of the governing equation of rarefied gas pressure based on the non-dimensional modified Reynolds equation and the over relaxation iteration method,the grid planning within the calculation range,the static solution of boundary parameters and static solution of the numerical process.Finally,the solution program is analyzed.The experimental data in National Aeronautics and Space Administration(NASA)public literature are compared with the simulation results of this exploration,so as to judge the accuracy of the calculation process.The results show that under the same static load,the difference between the minimum film thickness calculated and the test results is not obvious;when the rotor speed of the bearing is 60000 r/min,the influence of the boundary slip effect increases with the increase of the micro groove depth on the flat foil surface;when the eccentricity or the micro groove depth of the bearing increases,the bearing capacity will be strengthened.When the eccentricity is 6µm and 14µm,the viscous friction torque of the new foil bearing increases significantly with the increase of the depth of the foil micro groove,but when the eccentricity is 22µm,the viscous friction torque does not change with the change of the depth of the foil micro groove.It shows that the bearing capacity and performance of foil bearing are improved.

随机环境中选举模型的Hydrodynamic极限

本文研究随机环境中选举模型的Hydrodynamic极限 .首先 ,我们通过图表示构造出随机环境中的选举模型 。

多类型模型的Hydrodynamic极限

本文研究一类具有平移不变有限程的变相速率和不同的扩散速率的多类型模型的Hydrodynamic行为。在合适的条件下。

New Derivation of Ordinary Differential Equations for Transient Free-Surface Green Functions

Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D Green function and all its spatial derivatives are a set of fourth-order ordinary differential equations, which are identical with that of Clement (1998). All of these results may be used to accelerate numerical computation for the time-domain boundary element method in marine hydrodynamics.

Mathematical Model of Hydrodynamic Torque Converter and Analytic Description of Streamline

The mathematical model of a 3-element centripetal-turbine hydrodynamic torque converter and analytic description of fluid flow inside the hydrodynamic torque converter are investigated. A new torus coordinate system is proposed so as to quantitatively describe fluid movement inside the hydrodynamic torque converter. The particle movement inside the hydrodynamic torque converter is decomposed into meridional component movement and torus component movement, and a universal meridional streamline equation is derived. According to the relationship between the converter wheel velocity polygon and its blade angle, a torus streamline differential equation is established. The universal meridional streamline equation is approximated with square polynomials. The approximation error curve is given and the percentage error is not greater than 0.86%. Considered as a function of polar angle, the blade angle cotangent of each converter wheel varies linearly with polar angle. By using integral calculus, torus streamline equations are obtained. As a result, the problem of difficult flow description of the hydrodynamic torque converter is solved and a new analytic research system is established.

ON PROBLEMS IN THE WEAKLY NONLINEAR THEORY OF HYDRODYNAMIC STABILITY AND ITS IMPROVEMENT

There are three main problems in the weakly nonlinear theory of hydrodynamic stability:(1)The ra- dius of convergence with respect to the perturbation parameter is too small and there is no concrete estimation for it.(2)The solution has a special structure, thus in general, it can not satisfy the initial condition posed by many practical problems.(3) When the linear part of its solution does not correspond to a neutral case. there are more than one way in determining the Landau constants, and practically no one knows which is the best way. In this paper, problems(1)and(2)are solved theoretically, and ways for its improvement have been proposed. By comparing the theoretical results with those obtained by numerical simulations, problem(3)has also been clari- fied.

LARGE-TIME BEHAVIOR OF SOLUTIONS OF QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

A one-dimensional quantum hydrodynamic model （or quantum Euler-Poisson system） for semiconductors with initial boundary conditions is considered for general pressure-density function. The existence and uniqueness of the classical solution of the corresponding steady-state quantum hydrodynamic equations is proved. Furthermore, the global existence of classical solution, when the initial datum is a perturbation of t he steadystate solution, is obtained. This solution tends to the corresponding steady-state solution exponentially fast as the time tends to infinity.

Research advances of un-symmetric constitutive theory of anisotropic viscoelastic liquids and its hydrodynamic behavior

Research advances of un-symmetric constitutive equation of anisotropic fluid,influence of un-symmetric stress tensor on material functions,vibrational shear flow of the fluid with small amplitudes and rheology of anisotropic suspension were reported.A new concept of simple anisotropic fluid was introduced.On the basis of anisotropic principle,the simple fluid stress behaviour was described by velocity gradient tensor F and spin tensor W instead of velocity gradient tensor D in the classic Leslie-Ericksen continuum theory.Two relaxation times analyzing rheological nature of the fluid and using tensor analysis a general form of the constitutive equation of co-rotational type was introduced.More general model LCP-H for the fluid was developed.The unsymmetry of the shear stress was predicted by the present continuum theory for anisotropic viscoelastic fluid-LC polymer liquids.The influence of the relaxation times on material functions was specially studied.It is important to study the unsteady vibrational rotating flow with small amplitudes,as it is a best way to obtain knowledge of elasticity of the LC polymer,i.e.dynamic viscoelasticity.For the shear-unsymmetric stresses,two shear stresses were obtained thus two complex viscosities and two complex shear modulus(i.e.first and second one) were introduced by the constitutive equation which was defined by rotating shear rate introduced by author.For the two stability problems of fluid,such as stability of hydrodynamic flow and orientational motion,were discussed.The results show that the polymer suspension systems exhibit anisotropic character.The PNC systems can exhibit significant shear-thinning effects.For more concentrated polymer nano-suspensions,the first normal stress difference change from positive to negative,which is similar to LC polymer behavior.