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Stability of multiquadric quasi-interpolation to approximate high order derivatives

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Science China mathematics 2010年第4期53卷 985-992页

作者： MA LiMin 1,2 & WU ZongMin 1,1 shanghai key laboratory for contemporary applied mathematics,School of Mathematical Sciences,Fudan University,shanghai 200433,China 2 Department of Information and Computer Science,Zhejiang Gongshang University,Hangzhou 310018,China shanghai key laboratory for contemporary applied mathematics School of Mathematical Sciences Fudan University

Numerical simulation of the high order derivatives based on the sampling data is an important and basic problem in numerical approximation,especially for solving the differential equations *** classical method is the divided difference ***,it has been shown strongly unstable in ***,it can only be used to simulate the lower order derivatives in *** simulate the high order derivatives,this paper suggests a new method using multiquadric *** stability of the multiquadric quasi-interpolation method is compared with the classical divided difference ***,some numerical examples are presented to confirm the theoretical *** theoretical results and numerical examples show that the multiquadric quasi-interpolation method is much stabler than the divided difference *** property shows that multiquadric quasi-interpolation method is an efficient tool to construct an approximation of high order derivatives based on scattered sampling data even with noise.

关键词： numerical differential radial basis functions (RBFs) Hardy’s multiquadric (MQ) quasiinterpolation divided difference method white noise expectation variance

A LATTICE BOLTZMANN METHOD FOR SIMULATION OF A THREE-DIMENSIONAL DROP IMPACT ON A LIQUID FILM

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Journal of Hydrodynamics 2008年第3期20卷 267-272页

作者： SHI Zi-yuan YAN Yong-hua YAN-G Fan QIAN Yue-hong HU Guo-hui shanghai Institute of applied mathematics and Mechanics Shanghai University Shanghai 200072 China shanghai key laboratory of Mechanics in Energy and Environment Engineering Shanghai 200072 China shanghai East Pump （Group） Co. Ltd Shanghai 201907 China

A single-phase free surface tracking model based on the Lattice Boltzmann Method （LBM）, which has capability of simulating liquid-gas system with the assumption that the gas phase has only negligible influence on the liquid phase, is utilized to simulate the flow of a drop impacting on a liquid film. Three typical outcomes in the flows, i.e., deposition, crown and splash, which have been observed in the previous experiments, are obtained in the present three dimensional numerical simulations. The numerical results are consistent with the experimental and analytical results available.

关键词： Lattice Boltzmann Method (LBM) drop impact two-phase flows thin film

A NEW CONTINUUM TRAFFIC MODEL WITH THE EFFECT OF VISCOSITY

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Journal of Hydrodynamics 2011年第2期23卷 164-169页

作者： SONG Tao LI Xing-li KUANG Hua DONG Li-yun shanghai Institute of applied mathematics and Mechanics Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University Shanghai 200072 China School of applied Science Taiyuan University of Science and Technology Taiyuan 030024 China College of Physics and Technology Guangxi Normal University Guilin 541004 China

Through considering the connection between microscopic car-following model and macroscopic continuum model, a new viscous vehicular flow model is proposed, in which the viscosity coefficient is determined by a more realistic constitutive relationship between averaged reaction time of drivers and the car density. Further analysis indicates that two traffic sound speeds in this viscous model may determine the existence and the stability of traveling wave solutions with an analytical method.

关键词： viscosity continuum traffic model reaction time traffic sound speed traveling wave

NONLINEAR WAVE INDUCED BY AN ACCELERATING CYLINDRICAL TANK

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Journal of Hydrodynamics 2002年第2期14卷 12-16页

作者： Shi, Xiao-Min Le, Jia-Chun An, Shu-Ping Inst. of Appl. Math. and Mech. Shanghai Univ. Shanghai 200072 China Lab. of Solid Mech. of Ministry Tongji Univ. Shanghai 200092 China

This paper presents a method for solving Lagrangian version of governing equations that allows boundary conditions at the free surface to be satisfied exactly, which is a three-dimensional generalization of a method first put forward by Stoker. Analytical expressions of nonlinear hydrodynamic pressure up to the third order and of free surface displacement up to the fourth order of an accelerating cylindrical tank were obtained. Here only the motions of objects in their early stage after initial impulses was considered. As a justification of the method, the important special case when the ratio of tank diameter to fluid depth tends to infinity was taken as an example, which shows that the linear hydrodynamic pressure obtained agrees completely with Westergaard or von Karman's classical result.

关键词： Boundary conditions Hydrodynamics Nonlinear systems Pressure Surfaces Tanks (containers)

ON NON-ISOTROPIC JACOBI PSEUDOSPECTRAL METHOD

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Journal of Computational mathematics 2008年第4期26卷 511-535页

作者： Benyu Guo Keji Zhang Department of mathematics,shanghai Normal University,shanghai 200234,China Scientific Computing key laboratory of shanghai Universities Division of Computational Science of E-Institute of shanghai Universities Department of mathematics Shanghai Normal University Shanghai 200234

In this paper, a non-isotropic Jacobi pseudospectral method is proposed and its appli- cations are considered. Some results on the multi-dimensional Jacobi-Gauss type interpolation and the related Bernstein-Jackson type inequalities are established, which play an important role in pseudospectral method. The pseudospectral method is applied to a twodimensional singular problem and a problem on axisymmetric domain. The convergence of proposed schemes is established. Numerical results demonstrate the efficiency of the proposed method.

关键词： Jacobi pseudospectral method in multiple dimensions Jacobi-Gauss type inter-polation Bernstein-Jackson type inequalities Singular problem Problem on axisymmetricdomain.

EXPERIMENTAL STUDY ON THE VORTEX FORMATION AND ENTRAINMENT CHARACTERISTICS FOR A ROUND TRANSVERSE JET IN SHALLOW WATER

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Journal of Hydrodynamics 2009年第3期21卷 386-393页

作者： FAN Jing-yu ZHANG Yan WANG Dao-zeng shanghai Institute of applied mathematics and Mechanics Shanghai University Shanghai 200072 China key laboratory of Advanced Display and System Applications Ministry of Education and SMIT Center School of Mechatronics Engineering and Automation Shanghai University Shanghai 200072 China

The vortex formation and entrainment characteristics for a round transverse jet in shallow water were experimentally investigated by means of a combination of LIF flow visualization and PIV measurement. A scarf vortex wrapped around the main body of the jet is formed in the near-wall region due to the interaction between the resulting wall jet and sufficiently shallow crossflow, with some more or less unsteady flow properties and with spreading ranges as functions of both the velocity ratio and the water depth within the near field. The entrainment of the ambient crossflow fluid into the jet main body is closely associated with the time-evolving features of the shear layer between the jet and surrounding fluid as well as the induced vortical structures near the wall. In the case of slight impingement upon the wall, the interaction between the jet shear layer and the weak, unstable scarf vortex gives rise to an appreciable local entrainment enhancement, confined in the near-wall region in the vicinity of the stagnation point. While in the case of intense impingement upon the wall, the well-organized and stable scarf vortex gives rise to a greatly enhanced entrainment and a greatly increased lateral spreading rate nearly throughout the overall near field as compared to the conventional wall jet. In addition, the entrainment of the ambient crossflow fluid by the scarf vortex in this case occurs largely on the surface of the unique spiral roller structure by itself due to the presence of smaller and unorganized eddies, and accordingly the scarf vortex is likely to keep its spiral roller structure steadily to a relatively great downstream distance within the near field.

关键词： transverse jet shallow water vortex formation entrainment PIV measurement

Sharpness on the Lower Bound of the Lifespan of Solutions to Nonlinear Wave Equations

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Chinese Annals of mathematics,Series B 2011年第4期32卷 521-526页

作者： Yi ZHOU 1 Wei HAN 2 1 Nonlinear Mathematical Modeling and Methods laboratory shanghai key laboratory for Contem- porary applied mathematics School of Mathematical Sciences, Fudan University, shanghai 200433, China. 2 School of Mathematical Sciences, Fudan University, shanghai 200433, China Department of mathematics, North University of China, Taiyuan 030051, China. Nonlinear Mathematical Modeling and Methods laboratory Shanghai Key Laboratory for Contemporary Applied Mathematics School of Mathematical Sciences Fudan University Shanghai 200433 China

This paper is devoted to proving the sharpness on the lower bound of the lifespan of classical solutions to general nonlinear wave equations with small initial data in the case n = 2 and cubic nonlinearity （see the results of T. T. Li and Y. M. Chen in 1992）. For this purpose, the authors consider the following Cauchy problem： { where □=δt^2-∑i=1n δx^^2 is the wave operator, g（x）（≡/） 0 is a smooth non-negative function with compact support, and ε 〉 0 is a small parameter. It is shown that the solution blows up in a finite time, and the lifespan T（ε） of solutions has an upper bound T（ε） ≤ exp（Aε-2） with a positive constant A independent of ε, which belongs to the same kind of the lower bound of the lifespan.

关键词： Nonlinear wave equation Cauchy problem Lifespan

AN OPTIMIZATION OF EIGENFUNCTION EXPANSION METHOD FOR THE INTERACTION OF WATER WAVES WITH AN ELASTIC PLATE

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Journal of Hydrodynamics 2009年第4期21卷 526-530页

作者： XU Feng LU Dong-qiang shanghai Institute of applied mathematics and Mechanics Shanghai University Shanghai 200072 China State key laboratory of Ocean Engineering Shanghai Jiao Tong University Shanghai 200030 China

The hydroelastic interaction of an incident wave with a semi-infinite horizontal elastic plate floating on a homogenous fluid of finite depth is analyzed using the eigenfunction expansion method. The fluid is assumed to be inviscid and incompressible and the wave amplitudes are assumed to be small. A two-dimensional problem is formulated within the framework of linear potential theory. The fluid domain is divided into two regions, namely an open water region and a plate-covered region. In this paper, the orthogonality property of eigenfunctions in the open water region is used to obtain the set of simultaneous equations for the expansion coefficients of the velocity potentials and the edge conditions are included as a part of the equation system. The results indicate that the thickness and the density of plate have almost no influence on the reflection and transmission coefficients. Numerical analysis shows that the method proposed here is effective and has higher convergence than the previous results.

关键词： wave scattering eigenfunction expansion method orthogonality

LARGE-EDDY SIMULATION OF THREE-DIMENSIONAL VORTICAL STRUCTURES FOR AN IMPINGING TRANSVERSE JET IN THE NEAR REGION

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Journal of Hydrodynamics 2007年第3期19卷 314-321页

作者： FAN Jing-yu ZHANG Yan WANG Dao-zeng shanghai Institute of applied mathematics and Mechanics Shanghai University Shanghai 200072 China key laboratory of Advanced Display and System Applications （shanghai University） Ministry of Education and SMIT Center Shanghai University Shanghai 200072 China Department of applied Mechanics Chalmers University of Technology SE-412 96 Gothenburg Sweden shanghai Institute of applied mathematics and Mechanics Shanghai University Shanghai 200072 China

The three-dimensional vortical structures for an impinging transverse jet in the near region were numerically investigated by means of Large-Eddy Simulation （LES）. The LES results reproduced the skewed jet shear layer vortices close to the jet nozzle and the scarf vortex in the near-wall zone in good agreement with the experimental observations. Different vortical modes in the skewed jet shear layer close to the jet nozzle were identified depending upon the velocity ratio between jet and crossflow, namely changing from an approximately axisymmetric mode to a helical one with the velocity ratios varying from 20 to 8. Moreover, the scarf vortex wrapped around the impinging jet in the near-wall zone showed distinct asymmetry with regard to its bilateral spiral legs within the near region. And the entrainment of the ambient crossflow fluids by the scarf vortex in the near-wall zone was appreciably influenced by its asymmetry and in a large part occurred on the surface of the spiral roller structures in the course of spreading downstream.

关键词： Large-Eddy Simulation (LES) impinging jet crossflow vortical structure entrainment