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Applications of URANS on predicting unsteady turbulent separated flows

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Acta Mechanica Sinica 2009年第3期25卷 319-324页

作者： Jinglei Xu Huiyang Ma department of Physics, Graduate university of the Chinese Academy of sciences, 100049 Beijing, china department of Physics Graduate University of the Chinese Academy of Sciences Beijing China

Accurate prediction of unsteady separated turbulent flows remains one of the toughest tasks and a practi cal challenge for turbulence modeling. In this paper, a 2D flow past a circular cylinder at Reynolds number 3,900 is numerically investigated by using the technique of unsteady RANS （URANS）. Some typical linear and nonlinear eddy viscosity turbulence models （LEVM and NLEVM） and a quadratic explicit algebraic stress model （EASM） are evaluated. Numerical results have shown that a high-performance cubic NLEVM, such as CLS, are superior to the others in simulating turbulent separated flows with unsteady vortex shedding.

关键词： URANS Nonlinear eddy viscosity turbulencemodel ,Separated flows Circular cylinder

REGULARIZATION OF SINGULAR SYSTEMS BY OUTPUTFEEDBACK

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Journal of Computational Mathematics 2000年第1期18卷 43-60页

作者： De-lin Chu Da-yong Cai(department of Mathematical sciences, Tsinghua university, Beijing 100084, china) 清华大学北京 100084

Presents a study which examined problem of regularization of a singular linear time-invariant system by derivative and proportional output feedback. Reduced form for the system that can be computed using orthogonal tr... 详细信息

关键词： regularization singular systems output feedback

Input function and simulated distributions of tritium in the North Pacific

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Science china Earth sciences 2010年第3期53卷 441-453页

作者： BA Qi1,2 & XU YongFu1 1 State Key Laboratory of atmospheric Boundary Layer Physics and atmospheric Chemistry, Institute of atmospheric Physics, Chinese Academy of sciences, Beijing 100029, china 2 Graduate university of Chinese Academy of sciences, Beijing 100049, china State Key Laboratory of atmospheric Boundary Layer Physics and atmospheric Chemistry Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China Graduate university of Chinese Academy of sciences Beijing China

An ocean general circulation model (OGCM) of the North Pacific with a southern open boundary condition is used to simulate the distribution and transport of tritium in the North Pacific. First, the observed tritium in precipitation dataset of GNIP/ISOHIS is chosen, and used to develop an input function of tritium for the model domain from 1951 to 1997 in terms of the triangulation for interpolation. Then, the input function is used as an upper flux for the tritium model. The OGCM with tritium is integrated for 47 years with the initial condition of zero tritium concentrations. Compared with the observations from GEOSECS and WOCE, the model generates a meridional gradient of surface tritium concentrations and the high tritium concentrations in the subsurface layer, which is consistent with that indicated in the observations. The simulated time series of total tritium fluxes from the atmosphere to the ocean shows a spike in 1963. The total inventory of tritium in the ocean changes slowly with time after 1975. Tritium enters the higher-latitude region, and then is mainly transported by the subsurface process towards the equatorial region, which is well simulated in the model. However, the difference mainly occurs at 30°N–40°N, which can be seen also in the simulation of CFCs. This difference may partly originate from the insufficient description of physical processes in the OGCM. Nevertheless, some uncertainties exist in the development of the tritium input function, which can also influence the simulated results.

关键词： North Pacific basin-wide ocean general circulation model tritium input function tritium distributions

ELECTROCHEMICAL SYNTHESIS AND PROPERTIES OF POLY(AZURE B)

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Chinese Journal of Polymer Science 2001年第4期19卷 359-370页

作者： Dan Shan Shao-lin Mu department of Chemistry School of sciences, Yangzhou university Yangzhou 225002, china 扬州大学江苏扬州

A blue poly(azure B) film has been synthesized using repeated potential cycling between -0.25 and 1.10 V (versus SCE). The electrolytic solution consisted of 2.5 mmol dm(-3) azure B, 0.5 mol dm(-3) NaCl and 0.2 mol dm(-3) NaH2PO4 at the pH range of 2.0 to 11.0. The in situ visible spectrum during electrolysis of azure B shows that the intensity at 740 nm peak increases with increasing numbers of potential cycles, which is attributable to the formation of poly(azure B). The wavelength of its corresponding absorption peak is 98 nm longer than that of azure B. The polymerization rate is strongly affected by pH values. The anodic peak potential and cathodic peak potential of the poly(azure B) in a solution of pH 3.0 are not affected by increasing the scan rate from 25 to 600 mV s(-1). Poly(azure B) has good electrochemical reversibility and fast charge transfer characteristic in the pH range of 2.0 and 11.0. The conductivity of poly(azure B) is 1.5 x 10(-4) S cm(-1) According to the differences between FTIR spectra of poly(azure B) and azure B, an electrochemical polymerization mechanism of azure B is proposed in this paper.

关键词： azure B electrochemical polymerization electrochemical properties conductivity in situ UV-visible spectra FTIR spectra

SINE TRANSFORM MATRIX FOR SOLVING TOEPLITZ MATRIX PROBLEMS

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Journal of Computational Mathematics 2001年第2期19卷 167-176页

作者： Li-zhi Cheng (department of Mathematics & System sciences, National university of Defence Technology, Changsha 410073, china) 国防科技大学湖南长沙 410073

Provides information on a study which discussed the properties of eigenvalues for the solutions of symmetric positive definite Toeplitz systems, skew circulant and sine transform based properties. Eigenvalues of various preconditioners; Design of positive sine transform based preconditioners; Clustering property of the preconditioners; Numerical results.

关键词： preconditioner Toeplitz systems the fast sine transform conjugate gradient algorithm

SOBOLEV INEQUALITY ON RIEMANNIAN MANIFOLDS

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Chinese Annals of Mathematics,Series B 2005年第4期26卷 651-658页

作者： WANG MENG department of Mathematics, Zhejiang university, Hangzhou 310027, china School of Mathematical sciences, Pudan university, Shanghai 200433, china. department of Mathematics Zhejiang University Hangzhou 310027 China. School of Mathematical sciences Fudan University Shanghai 200433 China

Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(... 详细信息

关键词： Sobolev inequality Complete manifold Riesz transform Potential Heat kernel

Effects of salinity on methane gas hydrate system

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Science china Earth sciences 2007年第11期50卷 1733-1745页

作者： YANG DingHui1 & XU WenYue2 1 department of Mathematical sciences, Tsinghua university, Beijing 100084, china 2 School of Earth & atmospheric sciences, Georgia Institute of Technology, Atlanta, GA 30332, USA department of Mathematical sciences Tsinghua University Beijing China School of Earth & atmospheric sciences Georgia Institute of Technology Atlanta USA

Using an approximately analytical formation, we extend the steady state model of the pure methane hydrate system to include the salinity based on the dynamic model of the methane hydrate system. The top and bottom boundaries of the methane hydrate stability zone (MHSZ) and the actual methane hy-drate zone (MHZ), and the top of free gas occurrence are determined by using numerical methods and the new steady state model developed in this paper. Numerical results show that the MHZ thickness becomes thinner with increasing the salinity, and the stability is lowered and the base of the MHSZ is shifted toward the seafloor in the presence of salts. As a result, the thickness of actual hydrate occur-rence becomes thinner compared with that of the pure water case. On the other hand, since lower solubility reduces the amount of gas needed to form methane hydrate, the existence of salts in sea-water can actually promote methane gas hydrate formation in the hydrate stability zone. Numerical modeling also demonstrates that for the salt-water case the presence of methane within the field of methane hydrate stability is not sufficient to ensure the occurrence of gas hydrate, which can only form when the methane concentration dissolved in solution with salts exceeds the local methane solubility in salt water and if the methane flux exceeds a critical value corresponding to the rate of diffusive methane transport. In order to maintain gas hydrate or to form methane gas hydrate in marine sedi-ments, a persistent supplied methane probably from biogenic or thermogenic processes, is required to overcome losses due to diffusion and advection.

关键词： methane gas hydrate,solubility,stability of hydrate,salinity,phase equilibrium

The numbers of periodic orbits hidden at fixed points of 2-dimensional holomorphic mappings

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Science china Mathematics 2010年第3期53卷 863-886页

作者： ZHANG GuangYuan department of Mathematical sciences, Tsinghua university, Beijing 100084, china department of Mathematical sciences Tsinghua University

Let △n be the ball |x| < 1 in the complex vector space C n , let f :△n→ C n be a holomorphic mapping and let M be a positive integer. Assume that the origin 0 = (0, . . . , 0) is an isolated fixed point of both f and the M-th iteration f M of f. Then the (local) Dold index P M (f, 0) at the origin is well defined, which can be interpreted to be the number of virtual periodic points of period M of f hidden at the origin: any holomorphic mapping f 1 :△n→ C n sufficiently close to f has exactly P M (f, 0) distinct periodic points of period M near the origin, provided that all the fixed points of f M 1 near the origin are simple. Therefore, the number O M (f, 0) = P M (f, 0)/M can be understood to be the number of virtual periodic orbits of period M hidden at the fixed point. According to the works of Shub-Sullivan and Chow-Mallet-Paret-Yorke, a necessary condition so that there exists at least one virtual periodic orbit of period M hidden at the fixed point, i.e., O M (f, 0)≥1, is that the linear part of f at the origin has a periodic point of period M. It is proved by the author recently that the converse holds true. In this paper, we will study the condition for the linear part of f at 0 so that O M (f, 0)≥2. For a 2 × 2 matrix A that is arbitrarily given, the goal of this paper is to give a necessary and sufficient condition for A, such that O M (f, 0)≥2 for all holomorphic mappings f :△2 → C 2 such that f(0) = 0, Df(0) = A and that the origin 0 is an isolated fixed point of f M .

关键词： complex dynamical systems periodic points fixed point indices

On fixed-points and singular values of transcendental meromorphic functions

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Science china Mathematics 2010年第3期53卷 887-894页

作者： ZHENG JianHua department of Mathematical sciences, Tsinghua university, Beijing 100084, china department of Mathematical sciences Tsinghua University

In this paper we make a further discussion of a relationship between the number of fixed-points and distribution of singular values along the round annuli centered at the origin of a transcendental meromorphic function. To attain our purpose we first establish a fundamental inequality for the modulus of derivative of a holomorphic covering mapping whose image is an annulus by virtue of the hyperbolic metric. The inequality is of independent significance. We make a simple survey on some domain constants for hyperbolic domains.

关键词： meromorphic functions fixed points singular points hyperbolic metric covering mapping