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	1. Defects of Navier-Stokes Equations and a New Equation Set of Fluid Dynamics
	Xuegang Xie
	Mechanics 13 April 2007
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	Abstract:We point out that the conclusions derived from the Navier-Stokes equations are not in accordance with some basic experimental facts of the laminar-turbulent transition processes of shear flows, so they can not make the complete basis for describing the motion of fluids including the transition processes and the turbulence. According to the assumption of local equilibrium of non-equilibrium thermodynamics, under usual conditions, each small mass element of a fluid is in local equilibrium. Therefore it possesses not only a velocity of bulk translation, but also an angular velocity of bulk rotation. Based on this consideration, a new set of hydrodynamic equations which includes a balance equation of angular momentum is presented. For large-scale motions, it resumes the form of Navier-Stokes equations, but for small-scale motions, when the velocity shear increases to some extent, it will deviate from the Navier-Stokes equations significantly and exhibit new behaviors.
	TO cite this article:Xuegang Xie. Defects of Navier-Stokes Equations and a New Equation Set of Fluid Dynamics[OL].[13 April 2007] http://en.paper.edu.cn/en_releasepaper/content/12183


	2. GLOBAL SPATIAL DYNAMICS OF COUNTERCURRENT AXISYMMETRIC SHEAR FLOWS
	XiLin XIE,WeiWei MA,HuiLiang ZHOU
	Mechanics 16 February 2007
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	Abstract:
	TO cite this article:XiLin XIE,WeiWei MA,HuiLiang ZHOU. GLOBAL SPATIAL DYNAMICS OF COUNTERCURRENT AXISYMMETRIC SHEAR FLOWS[OL].[16 February 2007] http://en.paper.edu.cn/en_releasepaper/content/11174

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	3. Galilean invariance in two-dimensional lattice BGK models
	Ran zheng
	Mechanics 03 February 2007
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	Abstract:The Galilean invariance inherent in Navier-Stokes equations is not really recovered in two dimensional lattice Boltzmann equation, especially for shock calculation. This paper presents a systematic analysis on this subject.
	TO cite this article:Ran zheng. Galilean invariance in two-dimensional lattice BGK models [OL].[ 3 February 2007] http://en.paper.edu.cn/en_releasepaper/content/11027


	4. Lattice Boltzmann Thermohydro-dynamics and Galilean Invariance
	Zheng Ran
	Mechanics 26 January 2007
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	Abstract: From the point view of group-invairance, recovering the Galilean invariance for the isothermal LBGKE (Qian, D.d’Humieres, and P.Lallemand, 1992), induces a new natural thermal-dynamical system, which is compatible with the elementary statistical thermodynamics. New strategy for the thermal LBGKE calculation was also presented.
	TO cite this article:Zheng Ran. Lattice Boltzmann Thermohydro-dynamics and Galilean Invariance[OL].[26 January 2007] http://en.paper.edu.cn/en_releasepaper/content/10923


	5. Axial Couette Flow of Two Kinds of Fractional Viscoelastic
	Wang Shaowei,Xu Mingyu
	Mechanics 30 October 2006
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	Abstract:This paper deals with the unsteady axial Couette flow of fractional second grade fluid (FSGF) and fractional Maxwell fluid (FMF) between two infinitely long concentric circular cylinders. With the help of integral transforms (Laplace transform and Weber transform), generalized Mittag-Leffler function and H-Fox function, we get the analytical solutions of the models. Then we discuss the exact solutions and find some results which have been known as special cases of our solutions. Finally, we analyze the effects of the fractional derivative on the models by use of the numerical results and find that the oscillation exists in the velocity field of FMF.
	TO cite this article:Wang Shaowei,Xu Mingyu. Axial Couette Flow of Two Kinds of Fractional Viscoelastic[OL].[30 October 2006] http://en.paper.edu.cn/en_releasepaper/content/9123


	6. Large-Scale Dynamics of Isotropic Turbulence
	Ran Zheng
	Mechanics 17 May 2006
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	Abstract:The starting point for this paper lies in the results obtained by Sedov (1944) for isotropic turbulence with the self-preserving hypothesis. A careful consideration of the mathematical structure of the Karman-Howarth equation leads to an exact analysis of all possible cases and to all admissible solutions of the problem. This kind of appropriate manipulation escaped the attention of a number of scientists who developed the theory of turbulence and processed the experimental data for a long time. This paper revisits this interesting problem from a new point of view. Firstly, a new complete set of solutions are obtained, and Sedov’s solution is one special case of this set of solutions. Based on these exact solutions, some physically significant consequences of recent advances in the theory of self-preserved homogenous statistical solution of the Navier-Stokes equations are presented. New results could be obtained for the analysis on turbulence features, such as the scaling behavior, the spectrum, and also the large scale dynamics. Integral turbulence length scales based on the exact solutions are discussed, and used to derive rigorously a new recursion equation, which would be helpful in understanding the dynamical process of turbulence, especially for the Markov property and turbulence cascade. The general energy spectra and their behavior in the lowest wave number range are investigated. According to the present theory, the Loitsiansky integral is not an invariant in general cases.
	TO cite this article:Ran Zheng. Large-Scale Dynamics of Isotropic Turbulence[OL].[17 May 2006] http://en.paper.edu.cn/en_releasepaper/content/6657


	7. Similarity Solutions of Velocity Distributions in Homogeneous Isotropic Turbulence
	Ran Zheng
	Mechanics 05 May 2006
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	Abstract:The starting point for this paper lies in the results obtained by Tatsumi (2004) for isotropic turbulence with the self-preserving hypothesis. A careful consideration of the mathematical structure of the one-point velocity distribution function equation obtained by Tatsumi (2004) leads to an exact analysis of all possible cases and to all admissible solutions of the problem. This paper revisits this interesting problem from a new point of view. Firstly, a new complete set of solutions are obtained. Based on these exact solutions, some physically significant consequences of recent advances in the theory of homogenous statistical solution of the Navier-Stokes equations are presented. The comparison with former theory was also made. The origin of non-gaussian character could be deduced from the above exact solutions.
	TO cite this article:Ran Zheng. Similarity Solutions of Velocity Distributions in Homogeneous Isotropic Turbulence[OL].[ 5 May 2006] http://en.paper.edu.cn/en_releasepaper/content/6505


	8. Computing orientation distribution and rheology of turbulent fiber suspensions flowing through a contraction
	Lin Jianzhong
	Mechanics 27 February 2006
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	Abstract:The Reynolds averaged Navier-Stokes equation was solved with the Reynolds stress model to get the mean fluid velocity and the turbulent kinetic energy in the turbulent flow of a contraction with rectangular cross-section. The turbulent velocity fluctuations were represented as a Fourier series with random coefficients. Then the slender-body theory was used to predict the fiber orientation distribution, orientation tensor, additional shear stress and first normal stress difference of suspensions in the flow. Some numerical results are in agreement qualitatively with the experimental ones available in the literature. The results show that the longer fibers tend to align the streamline easily. Increased contraction ratio results in higher fiber alignment in the direction of flow. The fibers are weakly and strongly aligned in the direction of flow in the region near the inlet and the exit, respectively. Fibers are significantly more aligned in the plane of the contraction than they are aligned in the horizontal plane. Contraction ratio and fiber length were shown to strongly and weakly affect the distributions of additional shear stress and first normal stress difference.
	TO cite this article:Lin Jianzhong. Computing orientation distribution and rheology of turbulent fiber suspensions flowing through a contraction[OL].[27 February 2006] http://en.paper.edu.cn/en_releasepaper/content/5398


	9. Exact statistical theory of isotropic turbulence
	Ran Zheng
	Mechanics 12 January 2006
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	Abstract:Some physically significant consequences of recent advances in the theory of self-preserved homogenous statistical solutions of the Navier-Stokes equations are presented.
	TO cite this article:Ran Zheng. Exact statistical theory of isotropic turbulence[OL].[12 January 2006] http://en.paper.edu.cn/en_releasepaper/content/4988


	10. A Note on Harten’s Entropy Enforcement Condition
	Ran Zheng
	Mechanics 09 January 2006
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	Abstract:The theme of this paper is to understand the nonlinear stability properties of Harten’s TVD scheme from the point views of symmetry inherent in the PDE. Especial attentions are paid to Harten’s entropy enforcement condition. In this paper, we show that Harten’s entropy enforcement condition is consistent with the group invariant conditions.
	TO cite this article:Ran Zheng. A Note on Harten’s Entropy Enforcement Condition[OL].[ 9 January 2006] http://en.paper.edu.cn/en_releasepaper/content/4904

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