应用数学和力学

Goal-Oriented Error Estimation Applied to Direct Solution of Steady-State Analysis With Frequency Domain Finite Element Method

LIN Zhi-jia, YOU Xiao-chuan, ZHUANG Zhuo

2012, 33(5): 513-525. doi: 10.3879/j.issn.1000-0887.2012.05.001

Abstract(1758) PDF(806)

Abstract:
Based on the concept of constitutive relation error along with residual of both origin and dual problems, a goal-oriented error estimation method with extended degrees of freedom was developed. It leads to the high quality local error bounds in the problem of direct-solution steady-state dynamic analysis with frequency domain finite element, which involves enrichments with plural variable basis functions. The solution of steadystate dynamic procedure calculated the harmonic response directly in terms of the physical degrees of freedom in the model, which used mass, damping, and stiffness matrices of the system. An enriched form of goal-oriented error estimation aiming at this frequency calculation was formed and implemented. A three dimensional finite element example was carried out to illustrate the computational procedures.

Moment Liapunov Exponent of a Three-Dimensional System Under Bounded Noise Excitation

FANG Ci-jun, YANG Jian-hua, LIU Xian-bin

2012, 33(5): 526-538. doi: 10.3879/j.issn.1000-0887.2012.05.002

Abstract(1396) PDF(735)

Abstract:
The moment Liapunov exponent of a co-dimension two bifurcation system was evaluated, which was on a three-dimensional central manifold and was subjected to a parametric excitation by a bounded noise. Based on the theory of the stochastic dynamics, the eigenvalue problem governing the moment Liapunov exponent was established. Through a singular perturbation method, the explicit asymptotic expressions or numerical results of the second-order, weak noise expansions of the moment Liapunov are obtained for two cases. Then the effects of the bounded noise and the parameters of the system on the moment Liapunov exponent and the stability index were 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 Single Active Control

HE Gui-tian, LUO Mao-kang

2012, 33(5): 539-552. doi: 10.3879/j.issn.1000-0887.2012.05.003

Abstract(1567) PDF(831)

Abstract:
Along with the deepening of research on physics and technology,dynamics of fractional order nonlinear systems and synchronization of fractional order chaotic systems focus strong attention on itself. The dynamic behavior including chaotic properties of fractional order Duffing systems was extensively investigated and,via the stability criterion of linear fractional systems,the synchronization of a fractional nonautonomous system was obtained. Especially,a kind of effective singly active control was proposed and applied to synchronize the fractional order Duffing system. The corresponding numerical results demonstrated the effectiveness of the proposed methods.

Analysis of Radiometer Effect on the Proof Mass in Purely Gravitational Orbit

LIU Hong-wei, WANG Zhao-kui, ZHANG Yu-lin

2012, 33(5): 553-561. doi: 10.3879/j.issn.1000-0887.2012.05.004

Abstract(1484) PDF(820)

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

Lie Symmetry Group Transformation for MHD Natural Convection Flow of a Nanofluid Over a Linearly Porous Stretching Sheet in the Presence of Thermal Stratification

Abdul-Kahar Rosmila, Ramasamy Kandasamy, Ismoen Muhaimin

2012, 33(5): 562-573. doi: 10.3879/j.issn.1000-0887.2012.05.005

Abstract(1895) PDF(680)

Abstract:
The MHD convective flow and heat transfer of an incompressible viscous nanofluid past a semi infinite vertical stretching sheet in the presence of thermal stratification were examined. The partial differential equations governing the problem under consideration were transformed by a special form of Lie symmetry group transformations viz oneparameter group of transformation into a system of ordinary differential equations which were solved numerically using Runge Kutta Gill based shooting method. The conclusion is drawn that the flow field and temperature and nanoparticle volume fraction profiles are significantly influenced by thermal stratification and magnetic field.

Influence of Magnetic Field and Thermal Radiation by Natural Convection Past a Vertical Cone Subjected to a Variable Surface Heat Flux

G.Palani<, Kwang Yong Kim

2012, 33(5): 574-587. doi: 10.3879/j.issn.1000-0887.2012.05.006

Abstract(1553) PDF(639)

Abstract:
A numerical study was 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 was subjected to a variable surface heat flux. The fluid considered was a gray, absorbing-emitting radiation but a non-scattering medium, with approximate transformations the boundary layer equations governing the flow were reduced to a non-dimensional equations valid in the free convection regime. The dimensionless governing equations were solved by an implicit finite difference method of Crank-Nicolson type which is fast convergent, more accurate and unconditionally stable. Numerical results are obtained and presented for velocity, temperature, local and average wall shear stress, local and average Nusselt number in air and water. The present results are compared with the previously published work and are found to be in an excellent agreement.

A Two-Level Stabilized Finite Element Method for the Stokes Eigenvalue Problem

HUANG Peng-zhan, HE Yin-nian, FENG Xin-long

2012, 33(5): 588-597. doi: 10.3879/j.issn.1000-0887.2012.05.007

Abstract(2059) PDF(839)

Abstract:
A two-level stabilized finite element method for the Stokes eigenvalue problem based on local Gauss integration was considered. The method involved 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 an asymptotically optimal accuracy. The given method provided an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involved solving a Stokes eigenvalue problem on a fine mesh with mesh size h.Hence, the method can save a large amount of computational time. Moreover, numerical tests confirmed the theoretical results of the presented method.

MHD Stagnation Point Flow Towards a Heated Shrinking Surface Subject to Heat Generation/Absorption

2012, 33(5): 598-613. doi: 10.3879/j.issn.1000-0887.2012.05.008

Abstract(1567) PDF(623)

Abstract:
The magnetohydrodynamic (MHD) stagnation point flow of micropolar fluid towards a heated shrinking surface was analyzed. The effects of viscous dissipation and internal heat generation/absorption were taken into account. Two explicit cases of prescribed surface temperature (PST) and prescribed heat flux (PHF) were discussed. The boundary layer flow and energy equations were solved by employing a homotopy analysis method (HAM). The quantities of physical interest were examined through the presentation of plots/tabulated values. It was noticed that existing of solution for high shrinking parameter was associated closely with the applied magnetic filed.

Numerical Solution of Heat and Mass Transfer Problem in Oscillatory Flow of a Viscous Electrically Conducting Fluid Through a Porous Channel Subjected to a Magnetic Field: Applications to Blood Flow in Arteries in a Pathological State

A.Sinha, J.C.Misra

2012, 33(5): 614-627. doi: 10.3879/j.issn.1000-0887.2012.05.009

Abstract(1262) PDF(686)

Abstract:
A problem was motivated towards studying heat and mass transfer in the unsteady MHD flow of blood through a porous vessel, when the lumen of the vessel had turned into a porous structure. Consideration of time-dependent permeability and oscillatory suction velocity had been made. The problem was solved numerically. The computational results are presented graphically for the velocity, temperature and concentration fields as well as the skin friction co-efficient, Nusselt number and Sherwood number for various values of the parameters involved in the analysis.It was revealed 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 the Flow and Heat Transfer in a Micropolar Fluid Film Past a Moving Permeable Infinite Flat Plate With Slip Velocity

Mostafa A.A.Mahmoud, Shimaa E.Waheed

2012, 33(5): 628-642. doi: 10.3879/j.issn.1000-0887.2012.05.010

Abstract(1548) PDF(696)

Abstract:
The influence of thermal radiation on the problem of mixed convection thin film flow and heat transfer of a micropolar fluid past a moving infinite vertical porous flat plate with slip velocity was dealt with. The fluid viscosity and the thermal conductivity were assumed to vary as a function of temperature. The equations governing the flow were solved numerically using the Chebyshev spectral method for some representative value of various parameters. Comparisons with previously published work were performed and found to be in an excellent agreement. 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 were plotted and discussed.

2012 Vol. 33, No. 5