应用数学和力学

2011 Vol. 32, No. 12

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ZHANG Zhen-hua, WANG Yu, ZHANG Li-jun, YUAN Jian-hong, ZHAO Hai-feng

2011, 32(12): 1391-1404. doi: 10.3879/j.issn.1000-0887.2011.12.001

Abstract(1741) PDF(750)

Abstract:
The final anomalous sag distortion of ship girder subjected to near field underwater explosion (undex) below the middle ship was researched. Firstly, the sinking exercises of Spruance class destroyer DD973 sunk by one MK48 torpedo was presented and the simulation model was established. The exponential attenuation phase, reciprocal attenuation phase, post reciprocal attenuation phase and bubble pulse phase of undex load were precisely applied on this model. Fluid-solid interaction, added water mass, gravity and the change of buoyancy were also taken into account in this model. After that, the similarity theory was adopted to analyze the dynamic response of this ship girder. The similarity parameter and theory prediction formulae of the dynamic response of this ship girder were presented. Finally, the physical meaning and the influence of these similarity parameters were analyzed.

Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Boundary Integral Equations of Helmholtz Equation

CHENG Pan, HUANG Jin, WANG Zhu

2011, 32(12): 1405-1414. doi: 10.3879/j.issn.1000-0887.2011.12.002

Abstract(1818) PDF(835)

Abstract:
Mechanical quadrature methods(MQMs) for solving nonlinear boundary integral equations of Helmholtz equation, which possessed high accuracy order O (h³) and low computing complexities, were presented. Moreover, the mechanical quadrature methods were simple without computing any singular integration. A nonlinear system was constructed by discretizing the nonlinear boundary integral equations. The stability and convergence of the system were proved based on asymptotical compact theory and Stepleman theorem. Using the h³-Richardson extrapolation algorithms (EAs), the accuracy order to O (h⁵) was improved. For solving the nonlinear system, Newton iteration was discussed extensively by Ostrowski fixed point theorem. The efficiency of the algorithms was illustrated by numerical examples.

Momentum Equation for a Straight Electrically Charged Jet

ZHANG Ruo-jing, HOU Rui-hong, CHAN Cheong-ki

2011, 32(12): 1415-1423. doi: 10.3879/j.issn.1000-0887.2011.12.003

Abstract(1723) PDF(799)

Abstract:
A one-dimensional momentum conservation equation for a straight jet driven by an electrical field was developed. It was presented in terms of the stress component, which could be applied to any constitutive relation of fluids, and the only assumption was that the fluid was incompressible. Our results indicated that both the axial and the radial constitutive relations were required to close the governing equations of the straight charged jet. However, when the trace of the extra stress tensor was zero, only the axial constitutive relation was required. It was also found that the second normal stress difference for the charged jet was always zero. A comparison with other developed momentum equations was made.

Two-Scale Finite Element Method for Piezoelectric Problem in Periodic Structure

DENG Ming-xiang, FENG Yong-ping

2011, 32(12): 1424-1438. doi: 10.3879/j.issn.1000-0887.2011.12.004

Abstract(1858) PDF(766)

Abstract:
The prediction of the mechanical and electric properties of piezoelectric fibre composites had become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element method for solutions of the electric potential and the displacement for composite material in periodic structure under coupled piezoelectricity were derived. The coupled twoscale relation of the electric potential and the displacement was set up. And some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented.

Laguerre-Gauss Collocation Method for Initial Values Problems of Second Order ODEs

YAN Jian-ping, GUO Ben-yu

2011, 32(12): 1439-1460. doi: 10.3879/j.issn.1000-0887.2011.12.005

Abstract(1937) PDF(867)

Abstract:
Numerical method for initial value problems of second order ordinary differential equations was investigated. The new collocation method based on the Laguerre-Gauss interpolation was designed, which was very easy to be carried out, especially for nonlinear problems. The convergence was analyzed for two different cases, and the spectral accuracy was proved by using the recent results on the LaguerreGauss interpolation. A multi-step collocation method was also provided, which simplified actual computation and still kept the same spectral accuracy. The numerical results are presented, demonstrating the high accuracy of suggested algorithms.

Rotor Wake Capture Improvement Based on High Order Spatially Accurate Schemes and Chimera Grids

XU Li, WENG Pei-fen

2011, 32(12): 1461-1471. doi: 10.3879/j.issn.1000-0887.2011.12.006

Abstract(1541) PDF(730)

Abstract:
A high-order upwind scheme was developed to capture vortex wake of a helicopter rotor in hover based on chimera grids. An improved fifth-order weighted essentially non-oscillatory (WENO) scheme was adopted to interpolate higher-order left and right states across a cell interface with the Roe Riemann solver updating inviscid flux, and was compared with the monotone upwind scheme for scalar conservation laws (MUSCL). For profitably capturing the wake and enforcing period boundary condition, the computation regions of flows were discretized by using structured chimera grids composed of a fine rotor grid and a cylindrical background grid. In the background grid, the mesh cells located in the wake regions were refined after the solution reaches an approximate convergence. The optimized cylindrical mesh was attained by three remeshings. Considering the interpolation characteristic of WENO scheme, three layers of hole boundary and interpolation boundary were searched. The performance of the schemes was investigated in a transonic flow and a subsonic flow around hovering rotor. The results reveal that the present approach has the great capabilities to capture the vortex wake with high resolution, and WENO scheme has much lower numerical dissipation in comparison with MUSCL scheme.

Boundary-Layer Non-Newtonian Flow Over a Vertical Plate in a Porous Medium Saturated With a Nanofluid

F. M. Hady, F. S. Ibrahim, S. M. Abdel-Gaied, M. R. Eid

2011, 32(12): 1472-1480. doi: 10.3879/j.issn.1000-0887.2011.12.007

Abstract(1895) PDF(817)

Abstract:
The free convective heat transfer to the power-law non-Newtonian from a vertical plate in a porous medium saturated with nanofluid under laminar conditions was investigated. It was considered that the non-Newtonian nanofluid obeys the mathematical model of power-law. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The partial differential system governing the problem was transformed into an ordinary system via a usual similarity transformation. The numerical solutions of the resulting ordinary system were obtained. These solutions depend on the power-law index n, Lewis number Le, buoyancy-ratio number Nr, Brownian motion number Nb and thermophoresis number Nt. For various values of n and Le, the effect of the influence parameters on the fluid behavior as well as the reduced Nusselt number was presented and discussed.

Study on Stokes Flow of Micro-Polar Fluids by Peristaltic Pumping Through a Tube With Slip Boundary Condition

Dharmendra Tripathi, M. K. Chaube, P. K. Gupta

2011, 32(12): 1481-1493. doi: 10.3879/j.issn.1000-0887.2011.12.008

Abstract(1811) PDF(848)

Abstract:
The Stokes flow of micro-polar fluids by peristaltic pumping through the cylindrical tube under the effect of slip boundary condition was studied. The motion of wall was governed by the sinusoidal wave equation. Analytical and numerical solutions for axial velocity, micro-polar vector, stream function, pressure gradient, friction force and mechanical efficiency were obtained by using the lubrication theory. The impacts of emerging parameters such as coupling number, micro-polar parameter and slip parameter on pumping characteristic, friction force and trapping phenomena were depicted graphically. Numerical computation infers that more pressure requires for peristaltic pumping when coupling number is large while opposite behavior is found for micro-polar parameter and the slip parameter. The size of trapped bolus reduces with coupling number and micro-polar parameter whereas it blows up with slip parameter.

Mixed Convection Boundary Layer Flow Near the Stagnation Point on a Vertical Surface With Slip

Fazlina Aman, Anuar Ishak, Ioan Pop

2011, 32(12): 1494-1500. doi: 10.3879/j.issn.1000-0887.2011.12.009

Abstract(1688) PDF(796)

Abstract:
A steady mixed convection boundary layer flow of a viscous and incompressible fluid near the stagnation point on a vertical surface with slip effect at the boundary was considered. The temperature of the sheet and the velocity of the external flow were assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations were first transformed into a system of ordinary differential equations, which was then solved numerically by a shooting method. The features of the flow and heat transfer characteristics for different values of the governing parameters were analyzed and discussed. Both assisting and opposing flows were considered. The results indicate that for the opposing flow, dual solutions exist for a certain range of the buoyancy parameter, while for the assisting flow, the solution is unique. In general, the velocity slip increases the heat transfer rate at the surface, while the thermal slip decreases it.

Potential Symmetries and Conservation Laws for Generalized Quasilinear Hyperbolic Equations

M. Nadjafikhah, R. Bakhshandeh Chamazkoti, F. Ahangari

2011, 32(12): 1501-1508. doi: 10.3879/j.issn.1000-0887.2011.12.010

Abstract(1343) PDF(680)

Abstract:
Based on Lie group method, potential symmetry and invariant solutions for generalized quasilinear hyperbolic equations were studied. To obtain the invariant solutions in explicit form, the physically interesting situations which admit potential symmetries were studied. Then by using the partial Lagrangian approach, the conservation laws for the equation are found in three physically interesting cases.

Bifurcations of Traveling Wave Solutions and Exact Solutions of Generalized Zakharov Equation and Ginzburg-Landau Equation

DAI Zhen-xiang, XU Yuan-fen

2011, 32(12): 1509-1516. doi: 10.3879/j.issn.1000-0887.2011.12.011

Abstract(1538) PDF(970)

Abstract:
Some exact traveling wave solutions were found of generalized Zakharov equation and GinzburgLandau equation. What are the dynamical behavior of these traveling wave solutions and how do they depend on the parameters of the systems? These questions by using the method of dynamical systems were answered. Six exact explicit parametric representations of the traveling wave solutions for two equations were given.