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Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation

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Science China(Physics,Mechanics & Astronomy) 2005年第4期48卷 496-512页

作者： LI Zhihui1,2, ZHANG Hanxin1 & FU Song2 ⒈ National Laboratory for CFD, Hypervelocity Aerodynamics Institute,China Aerodynamics Research and Development Center,Mianyang 621000,China 2.Department of Engineering Mechanics,Tsinghua University,Beijing 100084,China National Laboratory for CFD Hypervelocity Aerodynamics Institute China Aerodynamics Research and Development Center Mianyang China Department of Engineering Mechanics Tsinghua University Beijing China

The gas-kinetic unified algorithm using Boltzmann model equation have been extended and developed to solve the micro-scale gas flows in Poiseuille-like micro-channels from Micro-Electro-Mechanical Systems (MEMS). The numerical modeling of the gas kinetic boundary conditions suitable for micro-scale gas flows is presented. To test the present method, the classical Couette flows with various Knudsen numbers, the gas flows from short microchannels like plane Poiseuille and the pressure-driven gas flows in two-dimensional short microchannels have been simulated and compared with the approximate solutions of the Boltzmann equation, the related DSMC results, the modified N-S solutions with slip-flow boundary theory, the gas-kinetic BGK-Burnett solutions and the experimental data. The comparisons show that the present gas-kinetic numerical algorithm using the mesoscopic Boltzmann simplified velocity distribution function equation can effectively simulate and reveal the gas flows in microchannels. The numerical experience indicates that this method may be a powerful tool in the numerical simulation of micro-scale gas flows from MEMS.

关键词： Boltzmann model equation, discrete velocity ordinate method, finite-difference scheme, Couette flow, Poiseuille flow, gas flow in short-microchannel.

Monotone method for initial value problem for fractional diffusion equation

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Science China Mathematics 2006年第9期49卷 1223-1230页

作者： ZHANG Shuqin Department of Mathematics China University of Mining and Technology Beijing 100083 China

Using the method of upper and lower solutions and its associated monotone iterative, consider the existence and uniqueness of solution of an initial value problem for the nonlinear fractional diffusion equation.

关键词： upper solutions and lower solutions, monotone iterative method, fractional diffusion equation, solution, existence and Uniqueness.

Reanalysis of the 3D quasi-stationary grain size distribution based on Hillert's grain growth rate equation

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Science China(Technological Sciences) 2004年第1期47卷 112-120页

作者： WANG Chao LIU Guoquan School of Materials Science and Engineering University of Science and Technology Beijing Beijing 100083 China School of Materials Science and Engineering University of Science and Technology Beijing Beijing 100083 China

Based on Hillert's 3D grain growth rate equation, the grain growth continuity equation was solved. The results show that there are an infinite number of 3D quasi-stationary grain size distributions. This conclusion ha... 详细信息

关键词： Hillert's grain growth equation, continuity equation, quasi-stationary state, grain size distribution, analytical distribution.

New Jacobian Elliptic Function Solutions to Modified KdV equation: Ⅰ

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Communications in Theoretical Physics 2002年第8期38卷 143-146页

作者： YAN Zhen-Ya Department of Applied Mathematics Dalian University of Technology Dalian 116024 China

An extended Jacobian elliptic function expansion method presented recently by us is applied to the mKdVequation such that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu's allresults are obtained. When the modulus m → 1 or 0, we can find the corresponding six solitary wave solutions and sixtrigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian ellipticfunction solutions and can be applied to other nonlinear differential equations.

关键词： modified KdV equation, Jacobian elliptic function, solitary wave solution, trigonometric functionsolution

Description of Rotational Molecular Spectra by the Two-Parameter Universal equation

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Communications in Theoretical Physics 2002年第8期38卷 209-212页

作者： ZENG Guo-Mo School of Physics and State Key Laboratory of Theoretical and Computational Chemistry Jilin University Changchun 130023 China

The n-power two-parameter universal equation for rotational spectra which we deduced recently is appliedto the description of the rotational bands of several diatomic and tetra-atomic molecules. Excellent agreement withexperimental data can be obtained with small n values. The relation between our equation and the famous Dunhamformula is discussed.

关键词： two-parameter equation, diatomic and tetra-atomic molecules, rotational spectra

Abundant Multisoliton Structures of the Generalized Nizhnik-Novikov-Veselov equation

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Communications in Theoretical Physics 2002年第10期38卷 395-399页

作者： ZHANG Jie-Fang CHEN Feng-Juan College of Mathematics Physics and Information Zhejiang Normal University Jinhua 321004 China Institute of Nonlinear Physics Zhejiang Normal University Jinhua 321004 China College of Mathematics Physics and Information Zhejiang Normal University Jinhua 321004 China

Using the extended homogenous balance method, we obtainabundant exact solution structures ofa (2+1)dimensional integrable model, the generalized Nizhnik-Novikov-Veselov equation. By means of the leading order termanalysis, the nonlinear transformations of generalized Nizhnik-Novikov-Veselov equation are given first, and then somespecial types of single solitary wave solution and the multisoliton solutions are constructed.

关键词： extended homogeneous balance method, (2+1) dimensions, NNV equation, soliton solutions

New Jacobian Elliptic Function Solutions of Modified KdV equation: Ⅱ

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Communications in Theoretical Physics 2002年第10期38卷 400-402页

作者： YAN Zhen-Ya Department of Mathematics University of British Columbia Vancouver BC Canada V6T 1Z2

Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by usingour extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and anotherthree families of new doubly periodic solutions (Jacobian elliptic function solutions) are fbund again by using a newtransformation, which and our extended Jacobian elliptic function expansion method form a new method still called theextended Jacobian elliptic function expansion method. The new method can be more powertul to be applied to othernonlinear differential equations.

关键词： modified KdV equation, Jacobian elliptic function, doubly periodic solution

Representation of the constitutive equation of viscoelastic materials by the generalized fractional element networks and its generalized solutions

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Science China(Physics,Mechanics & Astronomy) 2003年第2期46卷 145-157页

作者：徐明瑜谭文长 Institute of Mathematics and Systematical Science Research Center for Biomedical EngineeringShandong UniversityJinan 250100China Department of Mechanical Engineering Science Faculty of EngineeringKyushu UniversityFukuoka 812-8581JapanDepartment of Mechanics and Engineering SciencePeking UniversityBeijing 100871China

The generalized fractional element networks are presented in this paper. In order to extend the structure of the model solutions to the generalized function space and make it contain more physical meanings, the restriction on the parameters of the fractional element proposed by Schiessel et al. is eliminated and a 'compatibility equation' is added. The discretization method for solving the inverse Laplace transform is used and developed. The generalized solutions of the model equations are given. At the same time the generalized fractional element network--Zener and Poyinting-Thomson models are discussed in detail. It is shown that all the results obtained previously about the models of single parameter with fractional order and the classical models with integer order can be contained as the special cases of the results of this paper.

关键词： viscoelastic material, constitutive equation, generalized fractional element networks, fractional calculus, generalized solution.

Mathematical stencil and its application in finite difference approximation to the Poisson equation

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Science China Mathematics 2005年第10期48卷 1421-1429页

作者： FENG Hui~1 ZHANG Baolin~(1,2) & LIU Yang~1 1. Department of Mathematics,Wuhan University,Wuhan 430072,China 2. Laboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics,Beijing 100088. China Department of Mathematics Wuhan University Wuhan China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing China

The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented, and then a new type of the iteration algorithm is established for the Poisson equation. The new algorithm has not only the obvious property of parallelism, but also faster convergence rate than that of the classical Jacobi iteration. Numerical experiments show that the time for the new algorithm is less than that of Jacobi and Gauss-Seidel methods to obtain the same precision, and the computational velocity increases obviously when the new iterative method, instead of Jacobi method, is applied to polish operation in multi-grid method, furthermore, the polynomial acceleration method is still applicable to the new iterative method.

关键词： mathematical stencil, stencil elimination, Poisson equation, finite difference, iterative algorithm,parallelism.