应用数学和力学

2002 Vol. 23, No. 7

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High-Resolution Numerical Model for Shallow Water Flows and Pollutant Diffusions

WANG Jia-song, HE You-sheng

2002, 23(7): 661-666.

Abstract(2294) PDF(621)

Abstract:
A finite-volume high-resolution numerical model for coupling the shallow water flows and pollutant diffusions was presented based on using a hybrid TVD scheme in space discretization and a Runge-Kutta method in time discretization. Numerical simulations for modelling dam-break, enlarging open channel flow and pollutant dispersion were implemented and compared with experimental data or other published computations. The validation of this method shows that it can not only deal with the problem involving discontinuities and unsteady flows, but also solve the general shallow water flows and pollutant diffusions.

Studies On the Dynamic Buckling of Circular Plate Irradiated by Laser Beam

HUANG Chen-guang, DUAN Zhu-ping

2002, 23(7): 667-672.

Abstract(2057) PDF(468)

Abstract:
The dynamic buckling of thin copper plate induced by laser beam, was analyzed with the numerical integration and disturbance methods of controlling equation. The buckling and post-buckling of thin plate were shown, with the consideration of the temperature distribution, inertia effect and initial deflection. At last, the buckling criterion about the circular plate was obtained and used to investigate the relation between the critical laser intensity and the ratio of thickness and diameter of the plate. The results fit the experimental observation and the FEM simulation very well, and benefit to the understanding of failure phenomenon of structures irradiated by laser beam.

Numerical Solution of the Singularly Perturbed Problem With Nonlocal Boundary Condition

G. M. Amiraliyev, Musa ÇakIr

2002, 23(7): 673-681.

Abstract(2711) PDF(719)

Abstract:
Singularly perturbed boundary value problem with nonlocal conditions is examined. The appopriate solution exhibits boundary layer behavior for small positive values of the perturbative parameter. An exponentially fitted finite difference scheme on a non-equidistant mesh is constructed for solving this problem. The uniform convergence analysis in small parameter is given. Numerical example is provided, too.

Uzawa Type Algorithm Based on Dual Mixed Variational Formulation

WANG Guang-hui, WANG Lie-heng

2002, 23(7): 682-688.

Abstract(2595) PDF(497)

Abstract:
Based on the dual mixed variational formulation with three variants (stress, displacement, displacement on contact boundary) and the unilateral beaming problem of finite element discretization, an Uzawa type iterative algorithm is presented. The convergence of this iterative algorithm is proved, and then the efficiency of the algorithm is tested by a numerical example.

Two-Grid Error Estimates for the Stream Function Form of Navier-Stokes Equations

REN Chun-feng, MA Yi-chen

2002, 23(7): 689-696.

Abstract(2281) PDF(701)

Abstract:
The two-grid finite element approximation to the stream function form of the stationary Navier-Stokes equations was analyzed. The algorithms involve solving one small, nonlinear coarse mesh system, one linear problem on the fine mesh system, and a linear correct problem on the coarse mesh. The algorithms with the correct problem and without the correct problem were discussed. The algorithms produce an approximate solution with the optimal, asymptotic accuracy for any fixed Reynolds number.

A Nonlinear Galerkin/Petrov-Least Squares Mixed Element Method for the Stationary Navier-Stokes Equations

LUO Zhen-dong, ZHU Jiang, WANG Hui-jun

2002, 23(7): 697-706.

Abstract(2538) PDF(1215)

Abstract:
A nonlinear Galerkin/Petrov-least squares mixed element (NGPLSME) method for the stationary Navier-Stokes equations is presented and analyzed. The scheme is that Petrov-least squares forms of residuals are added to the nonlinear Galerkin mixed element method so that it is stable for any combination of discrete velocity and pressure spaces without requiring the Babu韐a-Brezzi stability condition. The existence, uniqueness and convergence (at optimal rate) of the NGPLSME solution is.

Rossby Inertia Gravity Solitary Wave and the Remote Correlation Between the East and the West-Pacific Subtropical High

ZHANG Ren, WANG Ji-guang, YU Zhi-hao, JIANG Quan-rong

2002, 23(7): 707-714.

Abstract(2311) PDF(568)

Abstract:
Based on the observational facts of seasonal abnormality of the west-pacifc subtropical high, considering a limited zonal belt under 500 hPa layer of north pacific subtropical area in summer,a kind of atmospheric solitary wave is found by applying a nonlinear shallow water model. The excitation, maintenance and propagation of this wave are closely correlated with the activity of middle-/east-pacific subtropical high. By discussing the propagation characters and computing the model atmospheric eigenvalue of the solitary wave, it is found that the route and range both the solitary wave and the atmospheric potential high center are comparatively identical in north-pacific subtropical area. The middle-/east-pacific subtropical high location/intensity. s normal or abnormal adjustment can possibly induce the west-pacific subtropical high being a corresponding variation or abnormity through the propagation mechanism of the solitary wave.

Extended Self Similarity of Passive Scalar in Rayleigh-Bénard Convection Flow Based on Wavelet Transform

FU Qiang, XIA Ke-qing

2002, 23(7): 715-721.

Abstract(1793) PDF(539)

Abstract:
Wavetet transform was used to analyze the scaling rule of temperature data (passive scalar) in Rayleigh-B nard convection flow from two aspects. The first one was to utilize the method of extended self similarity, presented first by Benzi et al, to study the scaling exponent of temperature data. The obtained results show that the inertial range is much wider than that one determined directly from the conventional structure function, and find the obtained scaling exponent agrees well with the one obtained from the temperature data in an experiment of wind tunnel. The second one was that,by extending the formula which was proposed by A. Armeodo et al for extracting the scaling exponent (q) of velocity data to temperature data, a newly defined formula which is also based to wavelet transform, and can determine the scaling exponent ξ(q) of temperature data was proposed. The obtained results demonstrate that by using the method which is named as WTNN (wavelet transfrom maximum modulus) ξ(q) correctly can be extracted.

Squeeze Flow of a Power-Law Fluid Between Two Rigid Spheres With Wall Slip

HUANG Wen-bin, XU yong, LIAN Guo-ping, LI Hong-yan

2002, 23(7): 722-728.

Abstract(2687) PDF(754)

Abstract:
The effect of wall slip on the squeeze flow of a power-law fluid between two rigid spherical particles has been examined based on the Reynolds lubrication theory. It is shown that the viscous force arising from the squeeze flow with wall slip may be resolved to the no-slip solution by introducing a slip correction coefficient. An expression for the slip correction coefficient of force is derived which is related to the slip parameter, the flow index and the upper limit of integration. Generally, wall slip results in a reduction in the viscous force. The reduction in the viscous force increases as the flow index increases, suggesting that wall slip has a more profound effect on shear thickening material. However, such reduction decreases as the upper limit of integration increases from finite liquid bridges to fully immersed systems. The reduction in the viscous force also increases as the slip parameter increases, which is the expected behaviour.

Time-Shifting Correcting Method of Phase Difference on Discrete Spectrum

DING Kang, LUO Jiang-kai, XIE Ming

2002, 23(7): 729-735.

Abstract(2562) PDF(1684)

Abstract:
A general method called time-shifting correcting method of phase difference on discrete spectrum is presented. That is, the second discrete-time sequence lags behind the first one with L points, then performing N-point FFT analysis on both sequences, and finally correcting spectrum by making use of the phase difference of two corresponding peak lines. The method proposed by XIE Ming et al is just the particular case of this method in the case that L is equal to N. Simulation result shows that this method is easily carried out with high precision, applicable for all kinds of symmetrical window functions and having high ability of anti-noise.

Modules Over Double Crossproducts of Skew-Hopf Pairs

PAN Qing-nian, HAO Zhi-feng

2002, 23(7): 736-742.

Abstract(2034) PDF(652)

Abstract:
The purpose is to study modules of double crossproducts D(X,A) of Skew-Hopf pairs (X,A). A sufficient and necessary condition for M to be D(X,A)-mod is shown. Relations between D(X,A)-mod and quantam Yang-Baxter A-mod or X-mod are revealed.

The Multi-Symplectic Algorithm for“Good” Boussinesq Equation

ZENG Wen-ping, HUANG Lang-yang, QIN Meng-zhao

2002, 23(7): 743-748.

Abstract(2538) PDF(633)

Abstract:
The multi-symplectic formulations of the/"Good" Boussinesq equation were considered.For the multi-symplectic formulation, a new fifteen-point difference scheme which is equivalent to the multi-symplectic Preissman integrator was derived. The numerical experiments show that the multisymplectic scheme have excellent long-time numerical behavior.

A Stress Vector-based Constitutive Model for Cohesionless Soil (Ⅱ)-Application

SHI Hong-yan, XIE Ding-yi, BAI Lin

2002, 23(7): 749-758.

Abstract(2765) PDF(703)

Abstract:
The stress vector-based constitutive model for cohesionless soil, proposed by SHI Hongyan et al, was applied to analyze the deformation behaviors of materials subjected to various stress paths. The result of analysis shows that the constitutive model can capture well the main deformation behavior of cohesionless soil, such as stress-strain nonlinearity, hardening property, dilatancy, stress path dependency, non-coaxiality between the principal stress and the principal strain increment directions, and the coupling of mean effective and deviatoric stress with deformation. In addition, the model can also take into account the rotation of principal stress axes and the influence of intermediate principal stress on deformation and strength of soil simultaneously. The excellent agreement between the predicted and measured behavior indicates the comprehensive applicability of the model.

Positive Solutions to a Singular Second Order Three-Point Boundary Value Problem

QU Wen-bo, ZHANG Zhong-xin, WU Jun-de

2002, 23(7): 759-770.

Abstract(2280) PDF(569)

Abstract:
A fixed point theorem is used to study a singular second order three-point boundary value problem. The problem is more general. Combining the method of constructing Green functions with operators defined piecewise, the existence result of positive solutions to a singular second order three-point boundary value probelm is established. The nonlinearity can be allowed to change sign.