Applied Mathematics and Mechanics (English Edition)

张振华汪玉张立军袁建红赵海峰

2011, 32(12): 1491-1504. doi:10.1007/s10483-011-1518-9

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The final anomalous sag distortion of the ship girder subjected to the near field underwater explosion (undex) below the middle ship is studied. The sinking exercise of Spruance class destroyer DD973 sunk by one MK48 torpedo is first presented, and a simulation model is established. The exponential attenuation phase, the reciprocal attenuation phase, the post reciprocal attenuation phase, and the negative pressure phase of the undex load are precisely applied in this model. The fluid-solid interaction, the added water mass, the gravity, and the change of buoyancy are also taken into account. The similarity theory is then used to analyze the dynamic response of the ship girder. Similarity parameters and theory prediction formulae of the dynamic response of the ship girder are presented. The physical meaning and influences of these similarity parameters are analyzed.

Mechanical quadrature methods and extrapolation for solving nonlinear boundary Helmholtz integral equations

程攀黄晋王柱

2011, 32(12): 1505-1514. doi:10.1007/s10483-011-1519-7

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This paper presents mechanical quadrature methods (MQMs) for solving nonlinear boundary Helmholtz integral equations. The methods have high accuracy of order O(h3) and low computation complexity. Moreover, the mechanical quadrature methods are simple without computing any singular integration. A nonlinear system is constructed by discretizing the nonlinear boundary integral equations. The stability and convergence of the system are proved based on an asymptotical compact theory and the Stepleman theorem. Using the h3-Richardson extrapolation algorithms (EAs), the accuracy to the order of O(h5) is improved. To slove the nonlinear system, the Newton iteration is discussed extensively by using the Ostrowski fixed point theorem. The efficiency of the algorithms is illustrated by numerical examples.

Momentum equation for straight electrically charged jet

张若京 S.H.HOU C.K.CHAN

2011, 32(12): 1515-1524. doi:10.1007/s10483-011-1520-9

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

Two-scale finite element method for piezoelectric problem in periodic structure

邓明香冯永平

2011, 32(12): 1525-1540. doi:34E13,35Q60,78M10,78M40

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The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic structure under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is 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 value problems of second order ODEs

严建平郭本瑜

2011, 32(12): 1541-1564. doi:10.1007/s10483-011-1522-x

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This paper proposes a new collocation method for initial value problems of second order ODEs based on the Laguerre-Gauss interpolation. It provides the global numerical solutions and possesses the spectral accuracy. Numerical results demonstrate its high efficiency.

Rotor wake capture improvement based on high-order spatially accurate schemes and chimera grids

徐丽翁培奋

2011, 32(12): 1565-1576. doi:10.1007/s10483-011-1523-6

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

Boundary-layer non-Newtonian flow over vertical plate in porous medium saturated with nanofluid

F.M.HADY F.S.IBRAHIM S.M.ABDEL-GAIED M.R.EID

2011, 32(12): 1577-1586. doi:10.1007/s10483-011-1524-7

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The free convective heat transfer to the power-law non-Newtonian flow from a vertical plate in a porous medium saturated with nanofluid under laminar conditions is investigated. It is 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 is transformed into an ordinary system via a usual similarity transformation. The numerical solutions of the resulting ordinary system are 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 effects of the influence parameters on the fluid behavior as well as the reduced Nusselt number are presented and discussed.

Stokes flow of micro-polar fluids by peristaltic pumping through tube with slip boundary condition

D.TRIPATHI M.K.CHAUBE P.K.GUPTA

2011, 32(12): 1587-1598. doi:10.1007/s10483-011-1525-6

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This paper studies the Stokes flow of micro-polar fluids by peristaltic pumping through the cylindrical tube under the effect of the slip boundary condition. The motion of the wall is governed by the sinusoidal wave equation. The analytical and numerical solutions for the axial velocity, the micro-polar vector, the stream function, the pressure gradient, the friction force, and the mechanical efficiency are obtained by using the lubrication theory under the low Reynolds number and long wavelength approximations. The impacts of the emerging parameters, such as the coupling number, the micro-polar parameter, the slip parameter on pumping characteristics, the friction force, the velocity profile, the mechanical efficiency, and the trapping phenomenon are depicted graphically. The numerical results infer that large pressure is required for peristaltic pumping when the coupling number is large, while opposite behaviors are found for the micro-polar parameter and the slip parameter. The size of the trapped bolus reduces with the increase in the coupling number and the micro-polar parameter, whereas it blows up with the increase in the slip parameter.

Mixed convection boundary layer flow near stagnation-point on vertical surface with slip

F. AMAN A. ISHAK I.POP

2011, 32(12): 1599-1606. doi:10.1007/s10483-011-1526-x

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This paper considers the steady mixed convection boundary layer flow of a viscous and incompressible fluid near the stagnation-point on a vertical surface with the slip effect at the boundary. The temperature of the sheet and the velocity of the external flow are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into a system of ordinary differential equations, which are then solved numerically by a shooting method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. The results indicate that for the opposing flow, the dual solutions exist in 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): 1607-1614. doi:10.1007/s10483-011-1527-6

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Based on the Lie group method, the potential symmetries and invariant solutions for generalized quasilinear hyperbolic equations are studied. To obtain the invariant solutions in an explicit form, the physically interesting situations with potential symmetries are focused on, and the conservation laws for these equations in three physically interesting cases are found by using the partial Lagrangian approach.

Bifurcations of traveling wave solutions and exact solutions to generalized Zakharov equation and Ginzburg-Landau equation

戴振祥徐园芬

2011, 32(12): 1615-1622. doi:10.1007/s10483-011-1528-9

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This paper studies the dynamic behaviors of some exact traveling wave solutions to the generalized Zakharov equation and the Ginzburg-Landau equation. The effects of the behaviors on the parameters of the systems are also studied by using a dynamical system method. Six exact explicit parametric representations of the traveling wave solutions to the two equations are given.

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