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Two-dimensional Riemann problems of simplified Euler equation

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chinese Science Bulletin 1998年第6期43卷 441-444页

作者： YANG Xiaozhou 1,2.and HUANG Feimin+1 1. institute of applied {2., chinese academy of sciences, beijing 100080, China 2. Department of {2., Shantou University, Guangdong 515063, China institute of applied {2. Chinese Academy of Sciences Beijing China Department of mathematics Shantou University Guangdong China

The two-dimensional Riemann problem of simplifed Euler equation is discussed, in which initial value contains two different constant states that are separated by a smooth curve. This problem is a natural description of realistic phenomena, but it is hard to study by conventional idea. So a new approach is proposed. Some new properties about two-dimensional rarefaction wave, shock wave and intermediate state of solutions are disclosed.

关键词： D Riemann problem implicit functions cylindrical surface pencil of cylindrical surface.

A predict-correct projection method for monotone variant variational inequalities

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chinese Science Bulletin 1998年第15期43卷 1264-1267页

作者： HAN Qiaoming 1 and HE Bingsheng 2.1. institute of applied {2., chinese academy of sciences, beijing 100080, China 2. Department of {2., Nanjing University, Nanjing 2.0093, China institute of applied {2. Chinese Academy of Sciences Beijing China Department of mathematics Nanjing University Nanjing China

A predict_correct projection method is presented for solving monotone variant variational inequalities, which could exploit the advantages and overcome the difficulties of both explicit and implicit projection methods.

关键词： variant variational inequality explicit projection method implicit projection method predict_correct projection method.

Global convergence property of s-dependent GFR conjugate gradient method

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chinese Science Bulletin 1998年第23期43卷 1959-1965页

作者： WANG Changyu 1,2.and ZHANG Yuzhong\+1 1. institute of Operations Research in Qufu Normal University, Qufu 2.3165, China 2. institute of applied mathematics,{2., beijing 100080, China institute of Operations Research Qufu Normal University Qufu China institute of applied {2. Chinese Academy of Sciences Beijing China

An \%S\%_dependent GFR method and a generalized conjugate gradient method are designed. Two estimated values of upper bounds for the ratio of β k to β FR k are given. The two convergence theorems are proved. The global convergent properties of \%s\%_dependent GFR method are obtained adopting several choice strategies of steplength and some results in recent literature are extended.

关键词： steplength linear search global convergence conjugate gradient.

Some key technics of drop tower experiment device of National Microgravity Laboratory (China) (NMLC)

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Science China(Technological sciences) 2005年第3期48卷 305-316页

作者： ZHANG Xiaoqian 1 , YUAN Longgen 1 , WU Wendong 1 , TIAN Lanqiao 2.& YAO Kangzhuang 2.1. institute of Engineering Thermophysics, chinese academy of sciences,{2., China 2. institute of Mechanics, chinese academy of sciences,{2., China 1. institute of Engineering Thermophysics Chinese Academy of Sciences 100080 Beijing China 2. institute of Mechanics Chinese Academy of Sciences 100080 Beijing China

Drop tower is an important ground based facility for microgravity science experiment. The technical performances of the drop tower NMLC are advanced compared with similar facilities in the US, Germany and Japan. The main components such as drop capsule, deceleration devices, release mechanism present its advantages and creativities.

关键词： drop tower facility,drop capsule,deceleration devices,release mechanism.

Algebraically explicit analytical solu-tions for the unsteady non-Newtonian swirling flow in an annular pipe

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Science China(Physics,Mechanics & Astronomy) 2006年第4期49卷 396-400页

作者： CAI Ruixian1 & GOU Chenhua1,2.1. institute of Engineering Thermophysics, chinese academy of sciences,{2., China 2. Graduate School, chinese academy of sciences,{2., China 1. institute of Engineering Thermophysics Chinese Academy of Sciences Beijing 100080 China 2. Graduate School Chinese Academy of Sciences Beijing 100080 China

This paper presents two algebraically explicit analytical solutions for the incompressible unsteady rotational flow of Oldroyd-B type in an annular pipe. The first solution is derived with the common method of separation of variables. The second one is deduced with the method of separation of variables with addition developed in recent years. The first analytical solution is of clear physical meaning and both of them are fairly simple and valuable for the newly developing computational fluid dynamics. They can be used as the benchmark solutions to verify the applicability of the existing numerical computational methods and to inspire new differencing schemes, grid generation ways, etc. Moreover, a steady solution for the generalized second grade rheologic fluid flow is also presented. The correctness of these solutions can be easily proven by substituting them into the original governing equation.

关键词： analytical solution, Oldroyd-B type fluid, swirling flow, non-Newtonian.

A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING THE ADVECTION-DIFFUSION EQUATIONS

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Journal of Computational mathematics 2002年第1期20卷 57-64页

作者： Huo-yuan Duan (institute of mathematics, {2. of mathematics and System sciences, chinese academy of sciences, beijing 100080, China) institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 北京 100080

Focuses on a study on the development of a stabilized finite element method for solving the advection-diffusion equations with a zero Dirichlet boundary condition. Problem formulation; Error analysis.

关键词： advection-diffusion equation stabilized finite element method

The proof of FFD(L)≤11/9OPT(L) +7/9

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chinese Science Bulletin 1997年第15期42卷 1262-1265页

作者： LI Rongheng, YUE Minyi1. Department of mathematics, Hunan Normal University, Changsha 410081, China 2. institute of applied mathematics,{2., beijing 100080, China Department of mathematics Hunan Normal University Changsha 410081 China institute of applied {2. Chinese Academy of Sciences Beijing 100080 China

THE one-dimensional bin-packing problem is defined as follows: for a given list L={p1, p2.…, Pn}, where 0i≤1 denotes the item and its size as well, we are to pack all the items in-to bins, each of which has a capaci... 详细信息

THE one-dimensional bin-packing problem is defined as follows: for a given list L={p1, p2./sub>,…, Pn}, where 0i≤1 denotes the item and its size as well, we are to pack all the items in-to bins, each of which has a capacity 1, and the goal is to minimize the number of bins *** first-fit-decreasing （FFD） algorithm is a famous approximate algorithm for the bin-pack-ing problem. The FFD algorithm first sorts all the list into non-increasing order and then pro-cesses the pieces in that order by placing each item into the first bin into which it fits.

关键词： bin-packing minimal counter-example weigtht-function FFD-algorithm.

Boundedness of solutions and existence of invariant tori for generalized pendulum type equation

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chinese Science Bulletin 1997年第20期42卷 1673-1675页

作者： HUANG Hai and YUAN Rong1. institute of mathematics,{2., beijing 100080, China 2. Department of mathematics, beijing Normal University, beijing 100875, China institute of mathematics Chinese Academy of Sciences Beijing China Department of mathematics Beijing Normal University Beijing China

MOTIVATED by various significant applications to non-Newtonian fluid theory, diffusion offlows in porous media, nonlinear elasticity, and theory of capillary surfaces, several authors(see refs.[1,2. and references cited therein ) have recently studied the existence of periodicsolutions and other properties for the following differential equation:

关键词： boundeduess of solutions invariant tori quasiperlodic solutions Moser’s small twist theorem.

Explicit analytical solutions of the anisotropic Brinkman model for the natural convection in porous media(Ⅱ)

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Science China(Physics,Mechanics & Astronomy) 2005年第4期48卷 422-430页

作者： CAI Ruixian1, GOU Chenhua1, 2.& ZHANG Na1 1. institute of Engineering Thermophysics, chinese academy of sciences,{2., China 2. Graduate School, chinese academy of sciences,{2., China 1. institute of Engineering Thermophysics Chinese Academy of Sciences 100080 Beijing China 2. Graduate School Chinese Academy of Sciences 10080 Beijing China

Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model―an improved Darcy model―describing the natural convection in porous media. Besides their important theoretical meaning (for example, in analyzing the non-Darcy and anisotropic effects on the convection), such analytical solutions can be the benchmark solutions that can promote the development of computational heat and mass transfer. Some solutions considering the anisotropic effect of permeability have been given previously by the authors, and this paper gives solutions including the anisotropic effect of thermal conductivity and the effect of heat sources.

关键词： explicit analytical solution, porous medium, natural convection, Brinkman model, anisotropic.