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Design of a new dynamical core for global atmospheric models based on some efficient numerical methods

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Science china mathematics 2004年第z1期47卷 4-21页

作者： WANG Bin, WAN Hui, Jl Zhongzhen, ZHANG Xin, YU Rucong, YU Yongqiang & LIU HongtaoState Key Laboratory of Numerical Modeling for Atmospheric sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese academy of sciences, Beijing 100029,{3. department of computational mathematics, academy of mathematics and system sciences, peking university, Beijing 100871,{3. Chinese Acad Sci Inst Atmospher Phys State Key Lab Numer Modeling Atmospher Sci & Geop Beijing 100029 Peoples R China peking Univ Acad Math & Syst Sci Dept Computat Math Beijing 100871 Peoples R China

A careful study on the integral properties of the primitive hydrostatic balance equations for baroclinic atmosphere is carried out, and a new scheme todesign the global adiabatic model of atmospheric dynamics ispresented. This scheme includes a method of weighted equal-areamesh and a fully discrete finite difference method with quadraticand linear conservations for solving the primitive equationsystem. Using this scheme, we established a new dynamical corewith adjustable high resolution acceptable to the availablecomputer capability, which can be very stable without anyfiltering and smoothing. Especially, some important integralproperties are kept unchanged, such as the anti-symmetries of thehorizontal advection operators and the vertical convectionoperator, the mass conservation, the effective energy conservationunder the standard stratification approximation, and so on. Somenumerical tests on the new dynamical core, respectively regardingits global conservations and its integrated performances inclimatic modeling, incorporated with the physical packagesfrom the Community Atmospheric Model Version 2 (CAM2) of NationalCenter for Atmospheric Research (NCAR), are included.

关键词： dynamical core, equal-area mesh, anti-symmetry, effective energy conservation.

CONVERGENCE OF VORTEX METHODS FOR 3.D EULER EQUATIONS

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Journal of computational mathematics 2000年第3期18卷 239-250页

作者： Jia-fu Lin (Institute of system Science, academy of mathematics and system sciences, Chinese academy of {3., Beijing, 100080, china School of Mathematical {3., peking university, Beijing 100871, china) 中科院系统科学所北京 100080

Presents a study on the convergence of vortex methods for the three-dimensional Euler equations in bounded domains. Related studies on the convergence of vortex methods; Formulation of vortex methods; Convergence for ... 详细信息

关键词： Euler equations vortex methods convergence initial-boundary value problem

Recovery of the scale-ε2 pattern by lattice BGK model

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Communications in Nonlinear Science and Numerical Simulation 2001年第1期6卷 40-44页

作者： Guangwu YAN and Li YUAN (Institute of computational mathematics, academy of mathematics and system sciences, Chinese {3. of sciences, Beijing 100080, china department of mathematics, Jinn university, Chongchun 13.023. china) Inst. of computational mathematics Acad. of Math. and System Sciences Chinese Academy of Sciences Beijing 100080 China department of mathematics Jilin University Changchun 130023 China

A lattice BGK method for nonlinear chemical reactions is described. Since the equation does not possess the convect terms, we can easily get the equilibrium distribution functions of the lattice BGK models. Using this... 详细信息

关键词： lattice BGK method Turing pattern mosaic structure

Line bundles on non-primary Hopf manifolds

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Science china mathematics 2004年第4期47卷 538-551页

作者： LIU Weiming & ZHOU XiangyuInstitute of mathematics, academy of mathematics and system sciences, Chinese academy of {3., Beijing 100080, china department of mathematics, Zhejiang university, Hangzhou 3.0028, china 1. Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China 2. department of mathematics Zhejiang University 310028 Hangzhou China

Let X be a Hopf manifolds with Abelian fundamental group, L any flat line bundle on X, we give a formula for computing explicitly the cohomology Hq(X, Ωp(L) using the method of group action and the generalized Douady... 详细信息

关键词： Hopf surface, cohomology, line bundle, sections.

CONVERGENCE OF CHORIN-MARSDEN FOR MULA FOR THENAVIER-STOKES EQUATIONS ON CONVEX DOMAINS

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Journal of computational mathematics 1999年第1期17卷 73-88页

作者： Lung-an Ying(Research institute for Mathematical sciences, Kyoto university, Japan department of {3., peking university, Beijing 100871, china) peking Univ Dept Math Beijing 100871 Peoples R China Kyoto Univ Math Sci Res Inst Kyoto Japan

We prove the convergence of the Chorin-Marsden product formula for solving the initial-boundary value problems of the Navier-Stokes equations on convex domains. As a particular case we consider the case of the half pl... 详细信息

关键词： Navier Stokes equation vortex method fractional step method convergence

Lattice Boltzmann solver of Rossler equation

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Communications in Nonlinear Science and Numerical Simulation 2000年第2期5卷 64-68页

作者： Guangwu YAN and Li RUAN (LSEC Institute of computational mathematics, academy of mathematics and system sciences, Chinese {3. of sciences, Beijing 100080, china department of mathematics, Jilin university, Changchun 13.023. china) LSEC Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China department of mathematics Jilin University Changchun 130023 China

We proposed a lattice Boltzmann model for the Rossler equation. Using a method of multiscales in the lattice Boltzmann model, we get the ditheion reaction as a special case. If the diffusion effect disappeared, we can obtain the lattice Boltzmann solution of the Rossler equation on the mesescopic scale. The numericale results show the method can be used to simulate Rossler equation.

关键词： lattice Boltzmann method multiscale technique Rossler equation

Lattice Boltzmann model for the perfect gas flows with near-vacuum region

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Communications in Nonlinear Science and Numerical Simulation 2000年第2期5卷 58-63页

作者： Guangwu YAN and Li YUAN (LSEC, Institute of computational mathematics, academy of mathematics and system sciences,Chinese {3. of sciences, Beijing 100080, china department of Mathermatics, Jilin university, Changchun 13.023. china) LSEC Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China department of mathematics Jilin University Changchun 130023 China

It is known that the standard lattice Boltzmann method has near-vacuum limit,i. e., when the density is near zero, this method is invalid. In this letter, we propose a shople lattice Boltzmann model for one-dimensional fiows. It possesses the ability of simulating near vacuum area by setting a limitation of the relaxation factor. Thus, the model overcomes the disadvantage of non-physical pressure and the density. The numerical examples show these results are satisfactory.

关键词： lattice Boltzmann method perfect gas near-vacuum region Roe’s tests

ON THE CENTRAL RELAXING SCHEME Ⅱ: systemS OF HYPERBOLIC CONSERVATION LAWS

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Journal of computational mathematics 2001年第6期19卷 571-582页

作者： Hua-zhong Tang (School of Mathematical sciences, peking university, Beijing 100871,{3.) (LSEC,ICMSEC academy of mathematics and systems sciences, Chinese academy of sciences, Beijing 100080,{3.) School of Mathematical sciences Peking University Beijing 100871 China

This paper continues to study the central relaxing schemes for system of hyperbolic conservation laws, based on the local relaxation approximation. Two classes of relaxing systems with stiff source term are introduced to approximate system of conservation laws in curvilinear coordinates. Based on them, the semi-implicit relaxing schemes are con- structed as in [6, 12] without using any linear or nonlinear Riemann solvers. Numerical experiments for one-dimensional and two-dimensional problems are presented to demon- strate the performance and resolution of the current schemes.

关键词： Hyperbolic conservation laws The relaxing system The central relaxing schemes The Euler equations.

ON THE HYPER ORDER OF SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS

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Chinese Annals of mathematics,Series B 2003年第4期24卷 501-508页

作者： CHEN ZONGXUAN department of mathematics, Jiangxi Normai university, Nanchang 3.0027,{3.. Institute of mathematics, academy of mathematics and system sciences, Chinese academy of sciences, Beijing 100080,{3.. Jiangxi Normal Univ Dept Math Nanchang 330027 Peoples R China Chinese Acad Sci Acad Math & Syst Sci Inst Math Beijing 100080 Peoples R China

The author investigates the hyper order of solutions of the higher order linear equation, andimproves the results of M. Ozawa[15], G. Gundersen[6] and J. K. Langley[12].

关键词： Differential equation Entire function Hyper order