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1.
This paper deals with the application of a moving mesh method for kinetic/hydrodynamic coupling model in two dimensions. With some criteria, the domain is dynamically decomposed into three parts: kinetic regions where fluids are far from equilibrium, hydrodynamic regions where fluids are near thermodynamical equilibrium and buffer regions which are used as a smooth transition. The Boltzmann-BGK equation is solved in kinetic regions, while Euler equations in hydrodynamic regions and both equations in buffer regions. By a well defined monitor function, our moving mesh method smoothly concentrate the mesh grids to the regions containing rapid variation of the solutions. In each moving mesh step, the solutions are conservatively updated to the new mesh and the cut-off function is rebuilt first to consist with the region decomposition after the mesh motion. In such a framework, the evolution of the hybrid model and the moving mesh procedure can be implemented independently, therefore keep the advantages of both approaches. Numerical examples are presented to demonstrate the efficiency of the method.  相似文献   

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The conclusions following from the solutions of the linearized hydrodynamic equations are discussed. By using some of symmetry properties of the Green functions the kinetic coefficients coupled to the external fields are determined and some interesting informations concerning the thermodynamic derivatives of the condensate density arise. A number of the Green functions is calculated in the hydrodynamic approximation. The examination of their denominators leads to the expressions for damping of the acoustic modes in He II-He3. A set of Kubo-type formulae for the kinetic coefficients and certain sum rules are obtained.  相似文献   

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Physics of the Solid State - The Kolmogorov–Feller and Einstein–Smoluchowski kinetic partial derivative equations with nonlinear coefficients are solved by new stable numerical methods....  相似文献   

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We have performed extensive numerical studies of Coulomb explosion of small molecules such as CO2 and N2O with the help of a hydrodynamic model, which allows one to deal with many-electron systems in intense laser fields. The predicted kinetic energy releases of the fragmentation channels are in good agreement with the measured energies, using realistic molecular and laser excitation condition parameters.  相似文献   

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In recent years it has become evident that fluctuating hydrodynamics predicts that fluctuations in nonequilibrium states are always spatially long ranged. In this paper we consider the application of fluctuating hydrodynamics to laminar fluid flow, using plane Couette flow as a representative example. Specifically, fluctuating hydrodynamics yields a stochastic Orr-Sommerfeld equation for the wall-normal velocity fluctuations, where spontaneous thermal noise acts as a random source.This stochastic equation needs to be solved subject to appropriate boundary conditions. We show how an exact solution can be obtained from an expansion in terms of the eigenfunctions of the Orr-Sommerfeld hydrodynamic operator. We demonstrate the presence of a flow-induced enhancement of the wall-normal velocity fluctuations and a resulting flow-induced energy amplification and provide a quantitative analysis how these quantities depend on wave number and Reynolds number.  相似文献   

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A shock wave that is characterized by sharp physical gradients always draws the medium out of equilibrium. In this work, both hydrodynamic and thermodynamic nonequilibrium effects around the shock wave are investigated using a discrete Boltzmann model. Via Chapman–Enskog analysis, the local equilibrium and nonequilibrium velocity distribution functions in one-, two-, and three-dimensional velocity space are recovered across the shock wave. Besides, the absolute and relative deviation degrees are defined in order to describe the departure of the fluid system from the equilibrium state. The local and global nonequilibrium effects, nonorganized energy, and nonorganized energy flux are also investigated. Moreover, the impacts of the relaxation frequency, Mach number, thermal conductivity, viscosity, and the specific heat ratio on the nonequilibrium behaviours around shock waves are studied. This work is helpful for a deeper understanding of the fine structures of shock wave and nonequilibrium statistical mechanics.  相似文献   

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A new kinetic equation is developed which incorporates the desirable features of the Enskog, the Rice-Allnatt, and the Prigogine-Nicolis-Misguich kinetic theories of dense fluids. Advantages of the present theory over the latter three theories are (1) it yields the correct local equilibrium hydrodynamic equations, (2) unlike the Rice-Allnatt theory, it determines the singlet and doublet distribution functions from the same equation, and (3) unlike the Prigogine-Nicolis-Misguich theory, it predicts the kinetic and kinetic-potential transport coefficients. The kinetic equation is solved by the Chapman-Enskog method and the coefficients of shear viscosity, bulk viscosity, thermal conductivity, and self-diffusion are obtained. The predicted bulk viscosity and thermal conductivity coefficients are singular at the critical point, while the shear viscosity and self-diffusion coefficients are not.  相似文献   

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Transverse mass spectra of pions and protons measured in central collisions of heavy ions at the SPS and at RHIC are compared to a hydrodynamic parameterization. While the chemical temperature needed at RHIC is significantly higher compared to SPS, the spectra may be described using kinetic freeze-out parameters which are similar for both beam energies. At RHIC either the temperature or the flow velocity is higher, but the data provide no unambiguous proof for much stronger transverse flow. The contribution of such hydrodynamic emission at high transverse momenta is investigated in detail. It is shown that hydrodynamics may be relevant up to relatively high transverse momenta. The importance of the velocity profile used in this context is highlighted. Received: 4 July 2002 / Revised version: 6 November 2002 / Published online: 20 December 2002  相似文献   

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《Physica A》1995,214(1):82-94
New terms describing dissipation are added to currents in the spin hydrodynamic equations for superfluid phases A and B of 3He. The terms contain kinetic coefficients connected with external magnetic field and nonconventional fields conjugated to the hydrodynamic variables describing suitable broken symmetries. Due to the Onsager type relations only two new coefficients in each phase (both connected with magnetic field) remain in the equations and can be expressed in terms of the “old” kinetic coefficients and some generalized susceptibilities. Experimental data for superfluid 3He may be able to provide information about “viscosity” of magnetic fields.  相似文献   

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The nonequilibrium equation of state is studied in the context of the hydrodynamic approach. The compression stage, the expansion stage, and the freeze-out stage of the hot spot formed during the collisions of heavy ions are considered. The energy spectra of protons and subthreshold pions produced in collisions of heavy ions are calculated with inclusion of the nuclear viscosity effects and compared with experimental data for various combinations of colliding nuclei with energies of several tens of MeV per nucleon.  相似文献   

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In this paper we derive rigorously the coupling of kinetic equations and their hydrodynamic limits for a simplified kinetic model. We prove the global convergence of the Chapman–Enskog expansion for this model. We then study the existence theory and asymptotic behaviour of the coupled systems. To solve the coupled problems we propose to use the transmission time marching algorithm. We then develop a convergence theory for the resulting algorithms.  相似文献   

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In this paper we study the hydrodynamic limit of a B.G.K. like kinetic model on domains with boundaries via BV loc theory. We obtain as a consequence existence results for scalar multidimensional conservation laws with kinetic boundary conditions. We require that the initial and boundary data satisfy the optimal assumptions that they all belong to L 1L with the additional regularity assumptions that the initial data are in BV loc . We also extend our hydrodynamic limit analysis to the case of a generalized kinetic model to account for forces effects and we obtain as a consequence the existence theory for conservation laws with source terms and kinetic boundary conditions.  相似文献   

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A derivation of hydrodynamic equations which describe diffusion in connection with reaction processes in many-particle systems is given on the basis of quantum kinetic theory. For this purpose kinetic equations are derived for a quantum gas with chemical reactions. Following Grad's method in a linear approximation reaction-diffusion equations can be obtained with explicite expressions for the diffusion and reaction rate coefficients. The influence of nonideality effects in reaction-diffusion equations is discussed.  相似文献   

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In this paper we show how using a relativistic kinetic equation the ensuing expression for the heat flux can be cast in the form required by Classical Irreversible Thermodynamics. Indeed, it is linearly related to the temperature and number density gradients and not to the acceleration as the so called “first order in the gradients” theories propose. Since the specific expressions for the transport coefficients are irrelevant for our purposes, the BGK form of the kinetic equation is used. Moreover, from the resulting hydrodynamic equations it is readily seen that the equilibrium state is stable in the presence of the spontaneous fluctuations in the transverse hydrodynamic velocity mode of the simple relativistic fluid. The implications of this result are thoroughly discussed.  相似文献   

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