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2012年 第33卷 第5期    刊出日期：2012-05-10

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论文

Goal-oriented error estimation applied to direct solution of steady-state analysis with frequency-domain finite element method

林治家;由小川;庄茁

2012, 33(5):  539-552.  doi:10.1007/s10483-012-1569-x

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Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It leads to the high quality local error bounds in the problem of the direct-solution steady-state dynamic analysis with a frequency-domain finite element, which involves the enrichments with plural variable basis functions. The solution of the steady-state dynamic procedure calculates the harmonic response directly in terms of the physical degrees of freedom in the model, which uses the mass, damping, and stiffness matrices of the system. A three-dimensional finite element example is carried out to illustrate the computational procedures.

Moment Lyapunov exponent of three-dimensional system under bounded noise excitation

方次军;杨建华;刘先斌

2012, 33(5):  553-566.  doi:10.1007/s10483-012-1570-9

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In the present paper, the moment Lyapunov exponent of a codimensional two-bifurcation system is evaluted, which is on a three-dimensional central manifold and subjected to a parametric excitation by the bounded noise. Based on the theory of random dynamics, the eigenvalue problem governing the moment Lyapunov exponent is established. With a singular perturbation method, the explicit asymptotic expressions and numerical results of the second-order weak noise expansions of the moment Lyapunov are obtained in two cases. Then, the effects of the bounded noise and the parameters of the system on the moment Lyapunov exponent and the stability index are investigated. It is found that the stochastic stability of the system can be strengthened by the bounded noise.

Dynamic behavior of fractional order Duffing chaotic system and its synchronization via singly active control

何桂添;罗懋康

2012, 33(5):  567-582.  doi:10.1007/s10483-012-1571-6

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With the increasingly deep studies in physics and technology, the dynamics of fractional order nonlinear systems and the synchronization of fractional order chaotic systems have become the focus in scientific research. In this paper, the dynamic behavior including the chaotic properties of fractional order Duffing systems is extensively investigated. With the stability criterion of linear fractional systems, the synchronization of a fractional non-autonomous system is obtained. Specifically, an effective singly active control is proposed and used to synchronize a fractional order Duffing system. The numerical results demonstrate the effectiveness of the proposed methods.

Analysis of radiometer effect on proof mass in purely gravitational orbit

刘红卫;王兆魁;张育林

2012, 33(5):  583-592.  doi:10.1007/s10483-012-1572-8

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Spacecrafts with the pure gravity environment are of great significance in precision navigation, gravity field measurement for celestial bodies, and basic physics experiments. The radiometer effect is one of the important interfering factors on the proof mass in a purely gravitational orbit. For the gravity field measurement system based on the inner-formation flying, the relationship between the radiometer effect on the innersatellite and the system parameters is studied by analytical and numerical methods. An approximate function of the radiometer effect suitable for the engineering computation and the correction factor are obtained. The analytic results show that the radiometer effect on the inner-satellite is proportional to the average pressure while inversely proportional to the average temperature in the outer-satellite cavity. The radiometer effect increases with the temperature difference in the cavity, and its minimum exists when the cavity radius increases. When the minimum of the radiometer effect arrives, the ratio of the cavity radius to the inner-satellite radius is 1.189 4. This constant is determined by the spherical cavity configuration and independent of the temperature and pressure distributions. When the ratio of the cavity radius to the inner-satellite radius is more than 10, it is believed that the cavity is large enough, the radiometer effect is approximately proportional to the square of the inner-satellite radius, and the influence of the outer-satellite cavity radius on the radiometer effect can be ignored.

Lie symmetry group transformation for MHD natural convection flow of nanofluid over linearly porous stretching sheet in presence of thermal stratification

A. B. ROSMILA;R. KANDASAMY;I. MUHAIMIN

2012, 33(5):  593-604.  doi:10.1007/s10483-012-1573-9

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The magnetohydrodynamics (MHD) convection flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the presence of thermal stratification are examined. The partial differential equations governing the problem under consideration are transformed by a special form of the Lie symmetry group transformations, i.e., a one-parameter group of transformations into a system of ordinary differential equations which are numerically solved using the Runge-Kutta-Gillbased shooting method. It is concluded that the flow field, temperature, and nanoparticle volume fraction profiles are significantly influenced by the thermal stratification and the magnetic field.

Influence of magnetic field and thermal radiation by natural convection past vertical cone subjected to variable surface heat flux

G. PALANI;K.Y.KIM

2012, 33(5):  605-620.  doi:10.1007/s10483-012-1574-7

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A numerical study is performed to examine the heat transfer characteristics of natural convection past a vertical cone under the combined effects of magnetic field and thermal radiation. The surface of the cone is subjected to a variable surface heat flux. The fluid considered is a gray, absorbing-emitting radiation but a non-scattering medium. With approximate transformations, the boundary layer equations governing the flow are reduced to non-dimensional equations valid in the free convection regime. The dimensionless governing equations are solved by an implicit finite difference method of Crank-Nicolson type which is fast convergent, accurate, and unconditionally stable. Numerical results are obtained and presented for velocity, temperature, local and average wall shear stress, and local and average Nusselt number in air and water. The present results are compared with the previous published work and are found to be in excellent agreement.

Two-level stabilized finite element method for Stokes eigenvalue problem

黄鹏展;何银年;冯新龙

2012, 33(5):  621-630.  doi:10.1007/s10483-012-1575-7

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A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h = O(H²), which can still maintain the asymptotically optimal accuracy. It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h. Hence, the two-level stabilized finite element method can save a large amount of computational time. Moreover, numerical tests confirm the theoretical results of the present method.

MHD stagnation point flow towards heated shrinking surface subjected to heat generation/absorption

T. HAYAT;M. HUSSAIN;A. A. HENDI;S. NADEEM

2012, 33(5):  631-648.  doi:10.1007/s10483-012-1576-6

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The magnetohydrodynamic (MHD) stagnation point flow of micropolar fluids towards a heated shrinking surface is analyzed. The effects of viscous dissipation and internal heat generation/absorption are taken into account. Two explicit cases, i.e., the prescribed surface temperature (PST) and the prescribed heat flux (PHF), are discussed. The boundary layer flow and energy equations are solved by employing the homotopy analysis method. The quantities of physical interest are examined through the presentation of plots/tabulated values. It is noticed that the existence of the solutions for high shrinking parameters is associated closely with the applied magnetic field.

Numerical study of flow and heat transfer during oscillatory blood flow in diseased arteries in presence of magnetic fields

A. SINHA;J. C. MISRA

2012, 33(5):  649-662.  doi:10.1007/s10483-012-1577-8

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A problem motivated by the investigation of the heat and mass transfer in the unsteady magnetohydrodynamic (MHD) flow of blood through a vessel is solved numerically when the lumen of the vessel has turned into the porous structure. The time-dependent permeability and the oscillatory suction velocity are considered. The computational results are presented graphically for the velocity, the temperature, and the concentration fields for various values of skin friction coefficients, Nusselt numbers, and Sherwood numbers. The study reveals that the flow is appreciably influenced by the presence of a magnetic field and also by the value of the Grashof number.

Variable fluid properties and thermal radiation effects on flow and heat transfer in micropolar fluid film past moving permeable infinite flat plate with slip velocity

M. A. A. MAHMOUD;S. E. WAHEED

2012, 33(5):  663-678.  doi:10.1007/s10483-012-1578-x

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This work deals with the influence of thermal radiation on the problem of the mixed convection thin film flow and heat transfer of a micropolar fluid past a moving infinite vertical porous flat plate with a slip velocity. The fluid viscosity and the thermal conductivity are assumed to be the functions of temperature. The equations governing the flow are solved numerically by the Chebyshev spectral method for some representative value of various parameters. In comparison with the previously published work, the excellent agreement is shown. The effects of various parameters on the velocity, the microrotation velocity, and the temperature profiles, as well as the skin-friction coefficient and the Nusselt number, are plotted and discussed.