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25 September 2008, Volume 25 Issue 5 Previous Issue    Next Issue

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Study on Finite Point Method LV Guixia, SHEN Longjun, SHEN Zhijun 2008, 25(5): 505-524.  Abstract ( )   PDF (841KB) ( )   A class of meshfree methods——finite point method on a set of two-dimensional disordered points is studied. Fundamentals of the method are established by means of directional differentials and directional differences. Formulae relating to multi-directional differentials of each order are given. Based on these formulae and with different numbers of neighboring points, five-peint formulae and less-point (two-point, three-point and four-point) formulae are derived, respectively. Solvability conditions of the five-point formulae and permissible set of neighboring points are discussed. Approximate expressions for classical differential operators on a set of disordered points are derived. It is demonstrated with theoretical analysis and numerical experiments that the accuracy of these formulae is improved as the number of neighboring points increases. These approximate formulae lay foundation for constructing computational schemes of partial differential equations on a set of disordered points. They can be applied to computational methods on unstructured meshes to increase accuracy as well.

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Two Schemes of Integrated Gradient Method YONG Heng, YUAN Guoxing, WANG Zheng 2008, 25(5): 525-534.  Abstract ( )   PDF (460KB) ( )   In a cylinderical coordinate system, integrated gradient method is an effective discrctization for equations of Lagrangian hydrodynamics. In the method IGT (Integral Gradient Total) scheme does not preserve spherical symmetry while IGA (Integral Gradient Average) scheme overcomes nonsymmetry in cylinderical coordinate system. However, IGA results in abnormally large acceleration in case of large mass ratios, where the mass of one subcell around a node is smaller than that of the other three subcells. If boundary force between neighbouring cells is taken as weighted mass average, IGA scheme is equivalent to IGT scheme in both a planar problem and a cylinderical problem even if there exists a large mass ratio. It is shown that IGT scheme preserves total momentum conservation but IGA scheme does not. Numerical results demonstrate advantages and disadvantages of the two schemes.

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Unified Method for Three-dimensional Moving Boundary in Lattice Boitzmann Method LIU Yanhua, LIN Jianzhong, KU Xiaoke 2008, 25(5): 535-542.  Abstract ( )   PDF (393KB) ( )   A unified method is proposed to treat 3D moving boundaries at arbitrary velocity as an extension of kinetic format and bounce-back format. Velocities at inlet and on solid wall are special cases of the model. A simplified expression is given in a three dimensional 15-velocity model. Numerical simulation for a diagonally lid-driven three-dimensional cavity flow is performed to verify this scheme. Compared with finite difference method (FDM), the proposed method proves reasonable.

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Stability of Normal Shock Waves in Viscous Materials YU Ming, LIU Fusheng 2008, 25(5): 543-548.  Abstract ( )   PDF (265KB) ( )   Stability of normal shock waves in viscous materials is analyzed with linear stability theory (LST). Equation of state of material adopts "stiff gas" expression. Stability problem of one-dimensional shock waves with arbitrary shock strength in viscous material is attribute to an eigenvalue problem with regard to complex number. The eigenvalue problem concerns two first-order ordinary differential equations and one second-order equation. Their coefficients depend on physics variables and gradients. The eigenvalue problem is discretized and solved in a four-order precision finite difference scheme. With analysis on stability of shock waves in aluminum under high pressure, it is shown that one dimensional shock wave is stable. It shows that the velocity of shock wave has opposite effects on attenuation of perturbation ahead and behind shock front. Viscosity of material makes the attenuation more rapidly.

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Transition and Turbulence/Shock Interaction in a Supersonic Boundary Layer Flow PAN Honglu, MA Handong, WANG Qiang 2008, 25(5): 549-554.  Abstract ( )   PDF (543KB) ( )   Shock/turbulent boundary layer interaction(STBLI) in a M∞=3.0 supersonic compression ramp flow are studied using a spatial large eddy simulation method. At upstream, flat plate transition and developed turbulent boundary layer are simulated in which Shock/turbulent boundary layer interaction shows at the ramp. Analysis on mechanism of turbulent boundary layer/shock interaction indicates that linear unstable disturbance leads transition rapidly. In the process of STBLI, average separation range of the ramp is smaller than that in the laminar flow. However, extent of the separation shows different characteristics in different span-wise positions due to high velocity strip and low velocity strip.

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Aerodynamic Force and Heat of Hypersonic Laminar and Turbulent Flows HE Xuzhao, ZHAO Huiyong, LE Jialing 2008, 25(5): 555-560.  Abstract ( )   PDF (325KB) ( )   A method using CFD technology is used for accurate prediction of aerodynamic force and heat of air-breathing hypersonic vehicles. It includes governing equations, turbulence models, advanced wall boundary condition and transition formulas. Heat flux and skin friction for typical laminar and turbulent flows of air-breathing vehicles are validated. Independence of heat flux and skin friction prediction with normal grids in turbulence flow is confirmed using wall function boundary. Aerodynamic heat and force of a designed air-breathing vehicle are simulated. Reliable numerical data for vehicle aerodynamic design and aerodynamic heat protection are provided.

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Three Dimensional Convective Heat Transfer in a Cubic Porous Enclosure:Inclination and Temperature Oscillation Frequency YANG Jian, ZENG Min, WANG Gang, WANG Qiuwang 2008, 25(5): 561-568.  Abstract ( )   PDF (538KB) ( )   Three dimensional unsteady natural convective heat transfer in an inclined cubic enclosure with porous medium is studied numerically. The right side wall (X=1) of the enclosure is kept at a constant temperature of To, Temperature of the opposite vertical wall (X=0) varies by sine law with a mean value of To. Other walls are kept adiabatic. A Brinkman-extended Darcy model is used to describe flow through porous medium in the enclosure and the equations are solved with SIMPLE algorithm. Inclination angle α1 rotating around Y coordinate varies between 0å and 90°. Inclination angle α2 rotating around X coordinate varies between 0° and 45°. Dimensionless temperature oscillation frequency f ranges from 5° to 90π. Effects of inclination angles and temperature oscillation frequency on heat transfer are studied in detail. It shows that the maximal heat transfer is achieved at an inclined angles α1=46°, α2=45° and a temperature oscillating frequency f=45π.

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SPH Method with Fully Variable Smoothing Lengths and Implementation QIANG Hongfu, GAO Weiran 2008, 25(5): 569-575.  Abstract ( )   PDF (506KB) ( )   SPH (smoothed particle hydrodnamics) method with fully variable smoothing lengths is proposed. Different from existing adaptive kernel SPH methods, fully variable smoothing lengths are considered based on an adaptive symmetrical kernel estimation. An evolution equation of density is derived which implicitly couples with a variable smoothing length equation. Based on Springel' s fully conservative formulation SPH momentum equation and energy equation are derived by using symmetrical kernel estimation instead of scatter kernel estimation. An additional iteration process is employed to solve evolution equations of density and variable smoothing lengths equation. SPH momentum equation and energy equation are solved explicitly. Computation cost added by iteration is little. The equations and algorithm are tested via three ID shock-tube problems and a 2D Sedov problem. It is showed that conservation of momentum and energy is improved substantially and variable smoothing lengths effect is corrected, especially in the 2D Sedov problem. Pressure peak position and pressure at center are more accurate than those by Springel's scheme. The method deals with large density gradient and large smoothing length gradient problems well, such as large deformation and serious distortion problems in high velocity impact and blasting.

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Numerical Study on Film Boiling with Interface Tracking YUAN Minghao, YANG Yanhua, LI Tianshu, HU Zhihua 2008, 25(5): 576-584.  Abstract ( )   PDF (468KB) ( )   A numerical method for simulation of interfacial flows with phase change is presented. A volume-of-fluid (VOF) method based on piecewise linear interface construction (PLIC) is used to track interface. Spocial treatment is taken to deal with discontinuous velocity field due to phase change at liquid-vapor interface. The treatment is easy and effective. SIMPLE method is used for flow field and a CSF model for surface tension. The method is used to simulate three-dimensional film boiling on a horizontal plate with Cartesian coordinates and axisymmetric two-dimensional natural convection film boiling on a hemisphericallyended rod with body fitted coordinates. They are in good agreement with analytical correlations.

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Efficient Strategy for Stress Distritution in Inverse Analysis of Sheet Metal Stamping TANG Bingtao, WANG Zhaoqing, LU Xiaoyang, ZHANG Yu 2008, 25(5): 585-590.  Abstract ( )   PDF (356KB) ( )   To overcome shortcomings of traditional inverse analysis method (TIAM), a fast and reliable searching scheme is used to find elements passing through die entrance radius during deformation process. An efficient stress-strain relation for continuous uniaxial tensile test is introduced to update stress distributions. Constitutive equations avoid complexity of incremental FEM based stress/strain updating algorithms, and effects of die entrance radius on deformation history are considered. Numisheet'93 square box drawing benchmark demonstrates that the constitutive equations significantly enhance prediction of stress distribution compared with incremental FEM based software DYNAFORM.

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Optical Property of a Liquid Crystal Cell with Grating Surface YE Wenjiang, XING Hongyu, YANG Guochen 2008, 25(5): 591-596.  Abstract ( )   PDF (257KB) ( )   With an equivalent anchoring energy formula for grating surface and elastic theory, a hybrid aligned nematic (HAN) liquid crystal cell proposed by Bryan-Brown et al is studied. Equations and boundary conditions for tilt angle and twist angle of director are obtained with variation theory. Tilt angle and twist angle of director with applied voltage at certain δ/λ are calculated with finite-difference iterative method. Electro-optical effect of liquid crystal cells is investigated with Jones matrix method. It depends on geometrical parameters of the grating surface, pitch λ and amplitude δ.

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EMC Characteristics of Multiple Airborne Antennas ZHAO Xunwang, LIANG Changhong, ZHANG Yu 2008, 25(5): 597-601.  Abstract ( )   PDF (301KB) ( )   In order to solve EMC problems for multiple antennas mounted on airborne platforms with limited computer resources, a multilevel fast multipole algorithm (MLFMA) with adaptive number of levels is implemented based on Electric Field Integral Equation(EFIE). For the analysis of coupling between antennas, more reasonable arbitrary isolation is adopted instead of traditional isolation. BiCGStab(l) combined with near-field preconditioner is employed which improves efficiency of the MLFMA. Radiation pattern and isolation of ultra-shortwave antennas on a full-scale Boeing 747 aircraft model are obtained and discussed.

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Laser Beam Propagation in Compressible Vortical Field MA Xiaoliang, YANG Guowei, SHEN Yiqing 2008, 25(5): 602-606.  Abstract ( )   PDF (265KB) ( )   A weakly-compressible two-dimensional axisymmetric isentropic vortex model is employed to stimulate interactions between single vortex and single optical wavefront. For near-field aero-optics at low beam energies geometrical optics is adopted. Optical-path-difference of propagated distorted wavefront is computed. It is confirmed that transform of beam wavefront is accelerated as beam passing through the vortex with low density. Single vortex defocuses the beam. Computation on COIL indicates that strength of vortex has strong effect on Strehl rate.

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Detuning in Open Four-level Inversionless Lasing Systems WANG Yong, LI Ping 2008, 25(5): 607-611.  Abstract ( )   PDF (227KB) ( )   A model for an open four-level atomic system driven by two fields is presented. Density matrix equations of motion are obtained by electric dipole and rotating wave approximations. Physical mechanism of lasing without inversion (LWI) is discussed. Effects of detuning on gain without inversion and population difference are studied. Dispersion equals to zero as two driving and probe fields are resonant. As one driving field (probe field) is resonant, the gain and the population difference versus detuning of driving field (probe field)show even symmetry, and the dispersion shows central symmetry. As two or three of driving and probe fields are off-resonance, the symmetries disappear. LWI gain is obtained when the dispersion equals to zero. When beth driving and probe fields are off-resonance, the gain, the dispersion and the population difference change greatly. High dispersion without absorption is obtained by adjusting suitable parameters of the system.

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Excited States of Plutonium Dioxide in External Electric Fields XIE Andong, ZHOU Lingling, WANG Zhenwu, ZHANG Aiyun, MAO Jinwen, LUO Wenlang, WU Donglan, RUAN Wen 2008, 25(5): 612-616.  Abstract ( )   PDF (262KB) ( )   Ground state of plutonium dioxide in electric fields ranging from-0.005 to 0.005 a.u. are optimized using density functional theory DFr/B3LYP with SDD for Pu and 6-311 + G* for O. Excitation energies in electric fields are calculated with time-dependent DFT method. It is shown that electronic state, total energy, molecular geometry, dipole moment and excitation energy are strongly dependent on the strength of applied electric field. Dependence of excitation energies on applied electric field strength agrees approximately with that proposed by Grozema. Spectra of the first five excited states are in the region of visible-infrared-far infrared with wavelength ranging from 501.47 to 10 291.5nm.

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Ground-state Energy of a Planar Quantum Dot with Two Electrons ZHENG Wenli, LI Zhiwen, SUN Yanxiu, LI Chunjiang 2008, 25(5): 617-622.  Abstract ( )   PDF (285KB) ( )   Ground-state energy of a planar quantum dot with two electrons is calculated with perturbation theory, numerically exact diagonalization and variational theory. Compared with earlier unrestricted Hartree-Fock studies, it is shown that a three-parameter variational wave function is an excellent representation of true ground state. It provides references for the understanding of planar quantum dots with more electrons.

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Phase Matching in Quantum Searching Algorithm with Weighted Targets LI Panchi, LI Shiyong 2008, 25(5): 623-630.  Abstract ( )   PDF (377KB) ( )   As searching targets in an unordered database with Grover's algorithm, difference in marked items is not taken into consideration. If fraction of marked items is greater than 1/4, success probability of search decreases rapidly with increase of marked items. When the fraction of marked items is greater than 1/2, the algorithm is disabled. Aiming at above problems, an improved Grover's algorithm with weighted targets is proposed in which every target is assigned a weight coefficient according to its significance. With these weight coefficients, targets are represented as quantum superpositions which make probability getting target equal to its weight coefficient. An adaptive phase matching method is proposed based on weighted targets. The directions of phase rotations are contrary, and amplitudes of the two phase rotations are determined by inner-product of target quantum superposition and initial state of the system. As the inner-product is greater than ((3-√5)/8)1/2, success probability is equal to 1 with two steps of Grover iteration at most. The improved quantum searching algorithm and the new phase matching are verified by an example.