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OPTIMAL MIXED H-P FINITE ELEMENT METHODS FOR STOKES AND NON-NEWTONIAN FLOW

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Journal of computational mathematics 2001年第1期19卷 67-76页

作者： Ping-bing Ming Zhong-ci Shi (institute of computational mathematics, chinese academy of sciences, beijing 100080, china) 中科院计算数学与工程计算数学所北京 100080

Presents an h -- p finite element methods based upon a mixed variational formulation for the three-field Stokes equations and linearized Non-Newtonian flow. Computation of the algebraic system generated from Problem H... 详细信息

关键词： mixed hp- finite element method non-Newtonian flow stabilization scaled weak B-Binequality

RADIAL BASIS FUNCTION INTERPOLATION IN SOBOLEV SPACES AND ITS APPLICATIONS

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Journal of computational mathematics 2007年第2期25卷 201-210页

作者： Manping Zhang (School of Mathematical sciences,Fudan University,Shanghai 200433,china institute of computational mathematics,chinese academy of sciences,beijing 100080,china School of Mathematical sciences Fudan University Shanghai 200433

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space H^k（Ω）（k 〉 1）. With a special kind of radial basis function, we construct a basis in H^k（Ω） and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density.

关键词： Sobolev space Radial basis function Global data density Meshless method

Numerical simulation of Richtmyer-Meshkov instability

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Science china mathematics 2004年第Z1期47卷 234-244页

作者： FU Dexun, MA Yanwen, ZHANG Linbo & TIAN BaolinState Key Laboratory of Nonlinear Mechanics, institute of Mechanics, chinese academy of sciences, beijing 100080, china State Key Laboratory of Scientific and Engineering Computing, institute of computational mathematics, chinese academy of sciences, beijing 100080, china State Key Laboratory of Nonlinear Mechanics Institute of Mechanics Chinese Academy of Sciences Beijing China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Chinese Academy of Sciences Beijing China

The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produced by cylindrical shock-cylindrical material interface with shock Mach number Ms=1.2 and density ratio 1:20 (interior density/outer density). Effect of shock refraction, reflection, interaction of the reflected shock with the material interface, and effect of initial perturbation modes on R-M instability are investigated numerically. It is noted that the shock refraction is a main physical mechanism of the initial phase changing of the material surface. The multiple interactions of the reflected shock from the origin with the interface and the R-M instability near the material interface are the reason for formation of the spike-bubble structures. Different viscosities lead to different spike-bubble structure characteristics. The vortex pairing phenomenon is found in the initial double mode simulation. The mode interaction is the main factor of small structures production near the interface.

关键词： R-M instability, direct numerical simulation, shock-interface interaction.

ON THE EXPLICIT COMPACT SCHEMES II: EXTENSION OF THE STCE/CE METHOD ON NONSTAGGERED GRIDS ON THE EXPLICIT COMPACT SCHEMES II: EXTENSION OF THE STCE/CE METHOD ON NONSTAGGERED GRIDS

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Journal of computational mathematics 2000年第5期18卷 467-480页

作者： Hua-zhong Tang , Hua-mu Wu (State Key Laboratory of Scientific and Engineering Computing, institute of computational mathematics, chinese academy of sciences, beijing 100080, china) 中科院计算数学所科学与工程计算国家重点实验室北京 100080

This paper continues to construct and study the explicit compact (EC) schemes for conservation laws. First, we axtend STCE/SE method on non-staggered grid, which has same well resolution as one in [1], and just requires half of the computational works. Then, we consider some constructions of the EC schemes for two-dimensional conservation laws, and some 1D and 2D numerical experiments are also given.

关键词： Conservation laws Compact scheme Shock-Capturing method Euler equations.

Systems Analysis for Economic Value of Water

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Systems Science and Systems Engineering 1999年第3期9卷 364-367页

作者： SHI Yao\|yuan institute of computational mathematics, chinese academy of sciences beijing 100080, china

Using the method of systems engineering we estimate the economic value of water in industry and in agriculture of Shanxi and give some important suggestion to save water.

关键词： translog production function shadow price input\|occupancy\|output table

NONCONFORMING QUADRILATERAL ROTATED ELEMENT FOR REISSNER-MINDLIN PLATE

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Journal of computational mathematics 2003年第1期21卷 25-32页

作者： Jun Hu Pingbing Ming Zhongci Shi (institute of computational mathematics, chinese academy of sciences, beijing 100080, china)

In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal H and L error bounds independent of the plate hickness are derived under a mild assumption on the mes... 详细信息

关键词： Reissner-Mindlin Plate Quadrilateral Rotated Q1 element Locking-free.

CASCADIC MULTIGRID FOR PARABOLIC PROBLEMS CASCADIC MULTIGRID FOR PARABOLIC PROBLEMS

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Journal of computational mathematics 2000年第5期18卷 551-560页

作者： Zhong-ci Shi, Xue-jun Xu (State Key Laboratory of Scientific and Engineering Computing, institute of computational mathematics, chinese academy of sciences, beijing 100080, china) 中科院计算数学所科学与工程计算国家重点实验室北京 100080

In this paper, we develop the cascadic multigrid method for parabolic problems. The optimal convergence accuracy and computation complexity are obtained.

关键词： Cascadic multigrid Finite element Parabolic problem.

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等谱流问题的李群算法

数值计算与计算机应用 2004年第4期25卷 295-302页

作者：田益民秦孟兆中国科学院软件研究所并行计算研究室北京100080 中科院计算数学研究所

In this paper, we studied the application of Lie group method in isospectral problem and we made numerical experiments by explicit Euler and implicit Euler with simple iteration and Newton iteration respectively:

关键词：等谱流李群算法非均匀介质声波传播微分方程初值问题

Multi-symplectic Schemes for Nonlinear wave Equation

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Multi-symplectic Schemes for Nonlinear wave Equation