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Numerical prediction of inner turbulent flow in conical diffuser by using a new five-point scheme and DLR k-ε turbulence model

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Journal of Central South University 2008年第S1期15卷 181-186页

作者：蒋光彪何永森舒适肖映雄 College of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University

The internal turbulent flow in conical diffuser is a very complicated adverse pressure gradient *** k-ε turbulence model was adopted to study *** every terms of the Laplace operator in DLR k-ε turbulence model and pressure Poisson equation were discretized by upwind difference scheme.A new full implicit difference scheme of 5-point was constructed by using finite volume method and finite difference method.A large sparse matrix with five diagonals was formed and was stored by three arrays of one dimension in a compressed *** iterative methods do not work wel1 with large sparse *** algebraic multigrid method(AMG),linear algebraic system of equations was solved and the precision was set at *** computation results were compared with the experimental *** results show that the computation results have a good agreement with the experiment *** precision of computational results and numerical simulation efficiency are greatly improved.

关键词： conical diffuser turbulent flow DLR k-ε turbulence model 5-point scheme algebraic multigrid method(AMG)

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A posteriori error estimates of spectral method for optimal control problems governed by parabolic equations

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science China Mathematics 2008年第8期51卷 1376-1390页

作者： CHEN YanPing HUANG YunQing YI NianYu School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105China

In this paper,we investigate the Legendre Galerkin spectral approximation of quadratic optimal control problems governed by parabolic equations.A spectral approximation scheme for the parabolic optimal control problem... 详细信息

关键词： Legendre Galerkin spectral method optimal control problems parabolic state equations a posteriori error estimates 49J20 65M60 65M70

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Numerical prediction of inner turbulent flow in conical diffuser by using a new five-point scheme and DLR k-ε turbulence model

Numerical prediction of inner turbulent flow in conical diff...

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The 9th National Conference on Rheology

The internal turbulent flow in conical diffuser is a very complicated adverse pressure gradient *** k-ε turbulence model was adopted to study *** every terms of the Laplace operator in DLR k-ε turbulence model and pressure Poisson equation were discretized by upwind difference scheme.A new full implicit difference scheme of 5-point was constructed by using finite volume method and finite difference method.A large sparse matrix with five diagonals was formed and was stored by three arrays of one dimension in a compressed *** iterative methods do not work well with large sparse *** algebraic multigrid method(AMG),linear algebraic system of equations was solved and the precision was set at *** computation results were compared with the experimental *** results show that the computation results have a good agreement with the experiment *** precision of computational results and numerical simulation efficiency are greatly improved.

关键词： conical diffuser turbulent flow DLR k-ε turbulence model 5-point scheme algebraic multigrid method（AMG）

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Preconditioners for higher order edge finite element discretizations of Maxwell's equations

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science China Mathematics 2008年第8期51卷 1537-1548页

作者： ZHONG LiuQiang1,2,SHU Shi1,2,SUN DuDu3&TAN Lin4 1School of Mathematical and computational sciences,Xiangtan University,Xiangtan 411105,China 2hunan key laboratory for computation and simulation in science and engineering,Xiangtan 411105,China 3Institute of computational Mathematics and Scientific/engineering Computing,Academy of Mathematicsand Systems science,Graduate University of Chinese Academy of sciences,Chinese Academy sciences,P.O.Box 2719,Beijing 100190,China 4Department of Math-Physics,Nanhua University,Hengyang 421001,China 1. School of Mathematical and Computational Sciences Xiangtan University Xiangtan 411105 China 2. Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan 411105 China 3. Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Graduate University of Chinese Academy of Sciences Chinese Academy Sciences P.O. Box 2719 Beijing 100190 China 4. Department of Math-Physics Nanhua University Hengyang 421001 China

In this paper,we are concerned with the fast solvers for higher order edge finite element discretizations of Maxwell's *** present the preconditioners for the first family and second family of higher order N′ed′elec element equations,*** combining the stable decompositions of two kinds of edge finite element spaces with the abstract theory of auxiliary space preconditioning,we prove that the corresponding condition numbers of our preconditioners are uniformly bounded on quasi-uniform *** also present some numerical experiments to demonstrate the theoretical results.

关键词： preconditioner higher order edge finite element stable decomposition

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Economical cascadic multigrid method (ECMG)

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science China Mathematics 2007年第12期50卷 1765-1780页

作者： Zhong-ci SHI~1 Xue-jun XU~(1+) Yun-qing HUANG~2 ~1 LSEC,Institute of computational Mathematics,Academy of Mathematics and Systems science,Chinese Academy of sciences,Beijing 100080,China ~2 hunan key laboratory for computation and simulation in science and engineering,Institute for computational and Applied Mathematics,Xiangtan University,Xiangtan 411105,China LSEC Institute of Computational Mathematics Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing 100080 China Hunan Key Laboratory for Computation Simulation in Science Engineering Institute for Computational Applied Mathematics Xiangtan University Xiangtan 411105 China

In this paper, an economical cascadic multigrid method is proposed. Compared with the usual cascadic multigrid method developed by Bornemann and Deuflhard, the new one requires less iterations on each level, especially on the coarser grids. Many operations can be saved in the new cascadic multigrid algorithms. The main ingredient is the control of the iteration numbers on the each level to preserve the accuracy without over iterations. The theoretical justification is based on the observations that the error reduction rate of an iteration scheme in terms of the smoothing property is no longer accurate while the iteration number is big enough. A new formulae of the error reduction rate is employed in our new algorithm. Numerical experiments are reported to support our theory.

关键词： economical cascadic multigrid method (ECMG), cascadic multigrid method (CMG)

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A UNIFIED A POSTERIORI ERROR ANALYSIS FOR DISCONTINUOUS GALERKIN APPROXIMATIONS OF REACTIVE TRANSPORT EQUATIONS

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Journal of computational Mathematics 2006年第3期24卷 425-434页

作者： Ji-ming Yang Yan-ping Chen Hunan Key Laboratory for Computation and Simulation in Science and Engineering Institute for Computational and Applied Mathematics and School of Mathematics and Computing Science Xiangtan University Xiangtan 4 11105 China

Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-BabuSka-Baumann DG （OBB-DG）, non-symmetric interior penalty Galerkin （NIPG）, symmetric interior penalty Galerkin （SIPG）, and incomplete interior penalty Galerkin （IIPG）. A unified a posteriori residual-type error estimation is derived explicitly for these methods. From the computed solution and given data, explicit estimators can be computed efficiently and directly, which can be used as error indicators for adaptation. Unlike in the reference [10], we obtain the error estimators in L^2 （L^2） norm by using duality techniques instead of in L^2（H^1） norm.

关键词： A posteriori error estimates Duality techniques Discontinuous Galerkin methods

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OPTIMAL ERROR ESTIMATES OF THE PARTITION OF UNITY METHOD WITH LOCAL POLYNOMIAL APPROXIMATION SPACES

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Journal of computational Mathematics 2006年第3期24卷 365-372页

作者： Yun-qing Huang Wei Li Fang Su Hunan Key Laboratory for Computation and Simulation in Science and Engineering Institute for Computational and Applied Mathematics Xiangtan University Xiangtan 4 11105 China Department of Computational Science Xiangtan University Xiangtan 4 11105 China

In this paper, we provide a theoretical method（PUFEM）, which belongs to the analysis of the partition of unity finite element family of meshfree methods. The usual error analysis only shows the order of error estimate to the same as the local approximations[12]. Using standard linear finite element base functions as partition of unity and polynomials as local approximation space, in l-d case, we derive optimal order error estimates for PUFEM interpolants. Our analysis show that the error estimate is of one order higher than the local approximations. The interpolation error estimates yield optimal error estimates for PUFEM solutions of elliptic boundary value problems.

关键词： Meshless methods Partition of unity finite element method（PUFEM） Error estimate.

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PRECONDITIONING HIGHER ORDER FINITE ELEMENT SYSTEMS BY ALGEBRAIC MULTIGRID METHOD OF LINEAR ELEMENTS

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Journal of computational Mathematics 2006年第5期24卷 657-664页

作者： Yun-qing Huang Shi Shu Xi-jun Yu Hunan Key Laboratory for Computation and Simulation in Science and Engineering Institute for Computational and Applied Mathematics Xiangtan University Xiangtan 411105 China Laboratory of Computational Physics Institute of Applied physics and Computational Mathematics Beijing 100088 China

We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm.

关键词： Finite element Algebraic multigrid methods Preconditioned Conjugate Gradient Condition number.

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An indirect convergent Jacobi spectral collocation method for fractional optimal control problems

An indirect convergent Jacobi spectral collocation method fo...

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作者： Yang, Yin Zhang, Jiaqi Liu, Huan O. Vasilev, Aleksandr Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan China Ammosov North-Eastern Federal University Yakutsk Russia

In this paper, we present a novel indirect convergent Jacobi spectral collocation method for fractional optimal control problems governed by a dynamical system including both classical derivative and Caputo fractional derivative. First, we present some necessary optimality conditions. Then we suggest a new Jacobi spectral collocation method to discretize the obtained conditions. By the proposed method, we get a system of algebraic equations by solving of which we can approximate the optimal solution of the main problem. Finally, we present a convergence analysis for our method and solve three numerical examples to show the efficiency and capability of the method. © 2019 John Wiley & Sons, Ltd.

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Spectral collocation method for a class of fractional diffusion differential equations with nonsmooth solutions

Spectral collocation method for a class of fractional diffus...

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作者： Wang, Junjie Xiao, Aiguo Bu, Weiping Hunan Key Laboratory for Computation and Simulation in Science and Engineering & Key Laboratory for Intelligent Computing and Information Processing of Education Ministry Xiangtan University Hunan China School of Mathematics and Statistics Pu'er University Yunnan China

In this paper, we develop spectral collocation method for a class of fractional diffusion differential equations. Since the solutions of these fractional differential equations usually exhibit singularities at the end-points, it can not be well approximated by classical polynomial basis functions. We first give nonclassical interpolants based on the associated Jacobi-Gauss points and obtain the corresponding fractional differentiation matrices. Second, we prove the convergence for the developed spectral collocation method. Finally, several numerical examples are considered to demonstrate the validity and applicability of the developed basis functions. © 2020 John Wiley & Sons, Ltd.

关键词： Polynomials

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