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A Functional Equation Governing the Motion of a compressible fluid Flow

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Tsinghua Science and Technology 2000年第2期5卷 154-158页

作者： M.H.MahmoudDepartment of Mathematical Sciences, Tsinghua University, Beijing 100084, China Department of Mathematical Sciences Tsinghua University Beijing 100084 China

The fundamental problem of the statistical dynamics of a turbulent flow, formulated in terms of characteristic functionals, has already been pointed out in the work of E. Hopf. In his work he deduced a functional equation governing the evolution of the characteristic functional of a turbulent velocity field in an incompressible field. In this paper we present a derivation of a dynamical equation governing the evolution of the characteristic functional of a turbulent velocity field in a compressible field. However, the characteristic functional equations we derived are governing the motions of an ideal gas and van der Waals gas.

关键词： characteristic functional dynamical equation compressible fluid

Numerical investigation of non-uniform temperature fields for proppant and fluid phases in supercritical CO_(2)fracturing

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Particuology 2024年第7期90卷 149-163页

作者： Boyu Liu Jun Yao Research Center of Multiphase Flow in Porous Media China University of Petroleum(East China)Qingdao 266000China

The non-uniform temperature distribution in supercritical CO_(2)(Sc-CO_(2))fracturing influences the density,viscosity,and volume expansion or shrinkage rate of Sc-CO_(2),impacting proppant *** study presents a coupled computational fluid dynamics-discrete element method and heat transfer model to examine the effects of proppant bed shape and the heat transfers of proppant-wall,proppant-fluid,and fluid-wall on the fluid and proppant temperature *** Sc-CO_(2)volume expansion is assessed under various temperature conditions by evaluating the volume-averaged Sc-CO_(2)*** factors,including proppant size,shape,thermal conductivity,concentration,temperature difference,and injection velocity,are carefully analyzed to elucidate their *** findings elucidate the existence of four distinct zones in the fluid temperature *** zone exhibits different magnitudes of temperature change under diverse conditions and undergoes dynamic transformations with the development of the proppant *** fluid-wall heat transfer and the fluid temperatures in Zones C and D are significantly subject to the fluid injection velocity(governing the heating duration),the temperature difference between fluid and formation(impacting the magnitude of heat flux),and the proppant bed shape(controlling the effective heating area).Additionally,the proppant-wall and proppant-fluid heat transfers determine the temperatures of both the proppant bed and the fluid within Zone B,showing a strong correlation with proppant thermal conductivity,proppant size,injection velocity,and temperature *** proposed coupled model provides valuable insights into the temperature distributions and flow behaviors of temperature-dependent fracturing fluids and proppants.

关键词： CFD-DEM Heat transfer compressible fluid CO_(2)sequestration Proppant transport

A Geometry-Preserving Finite Volume Method for compressible fluids on Schwarzschild Spacetime

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Communications in Computational Physics 2014年第3期15卷 827-852页

作者： Philippe G.LeFloch Hasan Makhlof Laboratoire Jacques-Louis Lions&Centre National de la Recherche Scientifique Université Pierre et Marie Curie(Paris 6)4 Place Jussieu75252 ParisFrance

We consider the relativistic Euler equations governing spherically symmetric,perfect fluid flows on the outer domain of communication of Schwarzschild spacetime,and we introduce a version of the finite volume method which is formulated from the geometric formulation(and thus takes the geometry into account at the discretization level)and is well-balanced,in the sense that it preserves steady solutions to the Euler equations on the curved geometry under *** order to formulate our method,we first derive a closed formula describing all steady and spherically symmetric solutions to the Euler equations posed on Schwarzschild ***,we describe a geometry-preserving,finite volume method which is based from the family of steady solutions to the Euler *** scheme is second-order accurate and,as required,preserves the family of steady solutions at the discrete *** experiments are presented which demonstrate the efficiency and robustness of the proposed method even for solutions containing shock waves and nonlinear interacting wave *** an application,we investigate the late-time asymptotics of perturbed steady solutions and demonstrate its convergence for late time toward another steady solution,taking the overall effect of the perturbation into account.

关键词： compressible fluid Euler system Schwarzschild spacetime geometry-preserving finite volume method steady state

FINITE ELEMENT ANALYSIS OF A VERTICAL RECTANGULAR PLATE COUPLED WITH AN UNBOUNDED fluid DOMAIN ON ONE SIDE USING A TRUNCATED FAR BOUNDARY

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Journal of Hydrodynamics 2009年第2期21卷 190-200页

作者： PANI P. K. BHATTACHARYYA S. K. Civil Engineering Department IGIT Sarang Orissa 759146 India Civil Engineering Department IIT Kharagpur 721302 India

The dynamic pressure distribution on a rectangular plate attached to a rigid wall and supporting an infinitely large extent of fluid subjected to a harmonic ground excitation is evaluated in the time domain. Governing equations for the fluid domain are set considering the compressibility of the fluid with negligibly small change in density and a linearized free surface. A far boundary condition for the three-dimensional fluid domain is developed so that the far boundary is truncated at a closer proximity to the structure. The coupled problem is solved independently for the structure and the fluid domain by transferring the acceleration of the plate to the fluid and pressure of the fluid to the plate in sequence. Helmholtz equation for the three-dimensional fluid domain and Mindlin＇s theory for the two-dimensional plate are used for the solution of the interacting domains. Finite element technique is adopted for the solution of this problem with pressure as nodal variable for the fluid domain and displacement for the plate. The time dependent equations are solved in each of the interacting domain using Newmark-fl method. The effectiveness of the technique is demonstrated and the influences of surface wave, exciting frequency and flexibility of the plate on dynamic pressure are investigated.

关键词： fluid-structure interaction compressible fluid linear surface wave truncation boundary dynamic pressure

ANALYSIS AND APPLICATION OF ELLIPTICITY OF STABILITY EQUATIONS ON fluid MECHANICS

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Applied Mathematics and Mechanics(English Edition) 2003年第11期24卷 1334-1341页

作者：李明军高智 LHD Institute of Mechanics Chinese Academy of Sciences Beijing 100080 P.R.China LHD Institute of Mechanics Chinese Academy of Sciences Beijing 100080 P.R.Chinay using characteristic analysis of the linear and nonlinear parabolic stability equations ( PSE) PSE of primitive disturbance variables are proved to be parabolic intotal. By using sub- characteristic analysis of PSE the linear PSE are proved to be elliptical and hyperbolic-parabolic for velocity U in subsonic and supersonic respectively the nonlinear PSE are proved to be elliptical and hyperbolic-parabolic for relocity U + u in subsonic and supersonic. respectively . The methods are gained that the remained ellipticity is removed from the PSE by characteristic and sub-characteristic theories the results for the linear PSE are consistent with the known results and the influence of the Mach number is also given out. At the same time the methods of removing the remained ellipticity are further obtained from the nonlinear PSE .

By using characteristic analysis of the linear and nonlinear parabolic stability equations ( PSE), PSE of primitive disturbance variables are proved to be parabolic intotal. By using sub- characteristic analysis of PSE, the linear PSE are proved to be elliptical and hyperbolic-parabolic for velocity U, in subsonic and supersonic, respectively; the nonlinear PSE are proved to be elliptical and hyperbolic-parabolic for relocity U + u in subsonic and supersonic., respectively . The methods are gained that the remained ellipticity is removed from the PSE by characteristic and sub-characteristic theories , the results for the linear PSE are consistent with the known results, and the influence of the Mach number is also given out. At the same time , the methods of removing the remained ellipticity are further obtained from the nonlinear PSE .

关键词： compressible fluid parabolic stability equation characteristic sub-characteristic

Stability of Weak Solutions for the compressible Navier-Stokes-Poisson Equations

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Acta Mathematicae Applicatae Sinica 2012年第3期28卷 597-606页

作者： Ru-xu LIAN Ming-jie LI College of Mathematics and Information Science North China University of Water Resources and Electric PowerZhengzhou 450011China School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

In this paper, we consider the isentropic compressible Navier-Stokes-Poisson equations arising from transport of charged particles or motion of gaseous stars in astrophysics. We are interested in the case that the viscosity coefficients depend on the density and shall degenerate in the appearance of （density） vacuum, and show the Ll-stability of weak solutions for arbitrarily large data on spatial multi-dimensional bounded or periodic domain or whole space.

关键词： compressible fluid Navier-Stokes-Poisson equations stability

Specific heat ratio effects of compressible Rayleigh—Taylor instability studied by discrete Boltzmann method

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Frontiers of physics 2021年第5期16卷 199-210页

作者： Lu Chen Huilin Lai Chuandong Lin Demei Li College of Mathematics and Statistics FJKLMAACenter for Applied Mathematics of Fujian Province(FJNU)Fujian Normal UniversityFuzhou350117China Sino-French Institute of Nuclear Engineering and Technology Sun Yat-sen UniversityZhuhai519082China

Rayleigh-Taylor(RT)instability widely exists in nature and engineering *** to better understand the physical mechanism of RT instability is of great theoretical significance and practical *** present,abundant results of RT instability have been obtained by traditional macroscopic ***,research on the thermodynamic non-equilibrium(TNE)effects in the process of system evolution is relatively *** this paper,the discrete Boltzmann method based on non-equilibrium statistical physics is utilized to study the effects of the specific heat ratio on compressible RT *** evolution process of the compressible RT system with different specific heat ratios can be analyzed by the temperature gradient and the proportion of the non-equilibrium ***,as a result of the competition between the macroscopic magnitude gradient and the non-equilibrium region,the average TNE intensity first increases and then reduces,and it increases with the specific heat ratio decreasing;the specific heat ratio has the same effect on the global strength of the viscous stress ***,the moment when the total temperature gradient in y direction deviates from the fixed value can be regarded as a physical criterion for judging the formation of the vortex ***,under the competition between the temperature gradients and the contact area of the two fluids,the average intensity of the non-equilibrium quantity related to the heat flux shows diversity,and the influence of the specific heat ratio is also quite remarkable.

关键词： discrete Boltzmann method Rayleigh-Taylor instability non-equilibrium effects specific heat ratio effects compressible fluid

WEAK TIME-PERIODIC SOLUTIONS TO THE compressible NAVIER-STOKES EQUATIONS

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Acta Mathematica Scientia 2016年第2期36卷 499-513页

作者：蔡虹谭忠 School of Mathematical Sciences Xiamen University School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and Scientific Computing Xiamen University

The compressible Navier-Stokes equations driven by a time-periodic external force are considered in this article. We establish the existence of weak time-periodic solutions and improve the result from [3] in the follo... 详细信息

关键词： compressible fluid Navier-Stokes equations weak time-periodic solutions

The Asymmetric Collapse of Bubbles in compressible Liquid

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Communications in Theoretical Physics 2003年第4期39卷 451-456页

作者： DUANWen－Shan DepartmentofPhysics NorthwestNormalUniversityLanzhou730070China

The analytical solution of a bubble collapse close to a solid boundary in a compressible water is investigated by means of a perturbation method to first order in the bubble wall Mach number. It is shown, in this paper, that it is the Rayleigh?Plesset equation for incompressible liquid to zero order solution or similar to the Gilmore equation for compressible water to first order solution when the effect of solid boundary is negligibly small enough, i.e., sufficiently far away from the bubble center.

关键词： bubble collapse compressible fluid