2013 Vol. 34, No. 5

Display Method:
Multi-Symplectic Leap-Frog Scheme for Sine-Gordon Equation
ZHANG Yu, DENG Zi-chen, HU Wei-peng
2013, 34(5): 437-444. doi: 10.3879/j.issn.1000-0887.2013.05.001
Abstract(1737) PDF(1508)
The nonlinear wave equation, which possesses various forms of analytical solutions, has been investigated widely in last several decades. The multi-symplectic method for the sine-Gordon equation in Hamilton space was proposed. Based on Hamiltonian variational principle, the multi-symplectic formulations of the sine-Gordon equation were deduced, and then, the leap-frog multi-symplectic discretization scheme was constructed using explicit symplectic discrete method. The numerical results for the sine-Gordon equation illustrate that the leap-frog multi-symplectic scheme can simulate the propagation of the soliton and the periodic solution for the sineGordon equation accurately, which show the superiority of the multi-symplectic algorithm when dealing with nonlinear evolution equations.
Lateral Capillary Forces Between Two Spherical Particles: a Lattice Boltzmann Study
LIANG Gong-you, ZENG Zhong, ZHANG Yong-xiang, ZHANG Liang-qi, XIE Hai-qiong, CHEN Yu
2013, 34(5): 445-453. doi: 10.3879/j.issn.1000-0887.2013.05.002
Abstract(1791) PDF(1694)
A three-dimensional simulation study on the lateral capillary forces (LCFs) between two floating and immersion spherical particles was carried out, using a modeling approach introduced in the framework of Shan-Chen lattice Boltzmann model for multi-component fluids. Solid-fluid interactions and wetting property of a colloidal particle could be taken into account at the mesoscopic level using a simple manner. Results show good agreement with theoretical results, and the so called “1/L” theory is demonstrated. At the same time, the linear relationship between immersion LCF and fluid interfacial tension for fixed interparticle distance is well achieved. These demonstrate that the model is a promising tool for the simulation of phenomenon such as self-assemblies of colloidal particles.
A Preconditioned Parallel Method for Solving Large Lyapunov Matrix Equation
HOU Jun-xia, Lü Quan-yi, CAO Fang-ying, XIE Gong-nan
2013, 34(5): 454-461. doi: 10.3879/j.issn.1000-0887.2013.05.003
Abstract(1422) PDF(1063)
A parallel algorithm with preconditioned modified conjugate gradient method for solving large Lyapunov matrix equation. The preconditioned Simth method for small matrix equation was first introduced, and then the modified conjugate gradient method was used for parallel solving the preconditioned Stein matrix equation, which transformed from the original Lyapunov matrix equation. To fix the involved difficulties such as the determination of the parameter μ and the solving inverse matrix of the matrix ( A +μ I ),Gerschgorin theorem and the modified conjugate gradient method were employed. Several numerical experiments show the proposed algorithm is superior to the modified conjugate gradient without precondition. The parallel efficiency is up to 0.85.
Trefftz Finite Element Analysis of Axisymmetric Potential Problems in Orthotropic Media
WANG Ke-yong, HUANG Zheng-ming, LI Pei-chao, LIU Bo
2013, 34(5): 462-469. doi: 10.3879/j.issn.1000-0887.2013.05.004
Abstract(1584) PDF(1518)
Trefftz finite element method (TFEM) has received considerable attention due to its excellent feasures. A four-node quadrilateral annular element was proposed for analyzing axisymmetric potential problems in orthotropic media. In the element model, two independent potential interpolation modes, namely intraelement field and frame field, were firstly assumed. Then, they were both substituted into the modified variational functional and the domain integral involved was eliminated using the Gaussian divergence theorem. Finally, the element stiffness equation including boundary integrals only was derived based on the stationary principle. Numerical examples demonstrate that the developed element is accurate, stable and insensitive to mesh distortion.
Explicit Form of Elastic Potentials Matching General Biaxial Test Data for Elastomers
LI Hao, ZHANG Yu-yu, XIAO Heng
2013, 34(5): 470-479. doi: 10.3879/j.issn.1000-0887.2013.05.005
Abstract(1255) PDF(1271)
A direct approach was proposed to construct elastic potentials that exactly match uniaxial data and shear data based on spline interpolation. Explicit expressions were presented toward bypassing complicated numerical procedures in identifying unknown parameters. Predictions for the two normal stresses of biaxial test were derived and compared with Rivlin and Saunders’ data in 1951. Good agreement was achieved.
Internal-External Combination Resonance of Nonlinear Vibration of in-Plane Translating Viscoelastic Plates
TANG You-qi, CHEN Li-qun
2013, 34(5): 480-487. doi: 10.3879/j.issn.1000-0887.2013.05.006
Abstract(1354) PDF(1072)
Nonlinear vibrations of inplane translating viscoelastic plates were investigated on the steady-state responses in external and internal resonances. The plate’s material obeys the Kelvin model in which the material time derivative was used. Based on the governing equation and boundary conditions for four edges simple supports, the method of multiple scales is applied to establish the solvability conditions in the primary resonance and the 3:1 internal resonance. The RouthHurvitz criterion is used to determine the stabilities of the steadystate responses. The effects of the viscosity coefficient, the in-plane translating speed, and the excitation amplitude on the steadystate responses are examined. The differential quadrature scheme is developed for the plate model to solve the nonlinear governing equations numerically. The numerical calculations confirm the approximate analytical results regarding the solutions of the steady- responses.
Finite Element Solution for Torsion Stress Function With Arbitrary Multi-Connected Section
WANG Jia-lin, HE Lin, ZHANG De-li
2013, 34(5): 488-495. doi: 10.3879/j.issn.1000-0887.2013.05.007
Abstract(1507) PDF(1510)
The major three methods can be used to solute the torsion bars’torsion problem. One is the boundary element method and the finite element method that is based on the warping function of torsion theory, the others are numerical solution based on the thinwall theory and the finite element method based on the torsion stress function of torsion theory. According to stress function theory of torsion bars with arbitrary cross section, a functional equivalent to the torsion’s differential equation and definite condition was discussed and improved, finite element formulas were deduced to solute the torsion stress function for multi-connected section, the boundary condition of single warping-displacement value was changed to concentrated force loaded on boundary nodes. The condition that the stress function must be constant value on each hole boundary was satisfied by using master-slave node method, so the torsion stress function with arbitrary multi-connected complex section could be obtained directly by finite element method, and the torsion constant was solved by integrating from the torsion stress function. Examples verified the feasibility and validity of this method.
Qualitative Analysis of Prey-Predator Model With Nonlinear-Impulsive Effects
WANG Gang, TANG San-yi
2013, 34(5): 496-505. doi: 10.3879/j.issn.1000-0887.2013.05.008
Abstract(1499) PDF(1151)
Due to the limited resources as well as the development of pests’ resistance to pesticides, the instant killing rate of pesticide applications with respect to the pest could depend on the density of pest populations. Thus, the instant killing rate is a function of economic threshold ET once the density of pest population reaches the ET and integrated control tactics are implemented. In order to depict the saturation effects, a prey-predator model with nonlinear state-dependent impulsive effects was proposed. Using the Lambert W function and the analytical techniques of the impulsive semi-dynamical system, the sufficient conditions which guaranteed the existence, local and global stability of order 1 positive periodic solution of the proposed model were obtained. Further, the effects of nonlinear impulse on the existence of order 1 periodic solution was discussed.
Apply the Multiple-Sets Split Feasibility Problem to CT Image Reconstruction
WANG Pei-yuan, ZHOU Hai-yun
2013, 34(5): 506-517. doi: 10.3879/j.issn.1000-0887.2013.05.009
Abstract(1334) PDF(1484)
To apply the CQ algorithm on the sparse angular CT image reconstruction better, a new realtime block successive mixed algorithm was proposed. Firstly, the problem of image reconstruction was transformed into the split feasibility problem. Secondly, through analyzing the different defines of nonempty closed convex sets C and Q,7 different implement cases in N dimension real space were proposed. Through simulations the convergence rate and reconstruction precision to different cases were analyzed, and how to select the constraint weights in algorithm and the output was studied. Then it obtain the best cases of CQ algorithm’s applying on sparse angular CT image reconstruction. Therefore, the best case of proposed algorithm is obtained. The results show that the proposed algorithm have faster convergence rate and better reconstruction precision. It proposes new ideas for applying the split feasibility problem and its extending norms to the CT incomplete projection data image reconstruction.
Weak Gorenstein Flat Modules Under the Left wGF-Closed Rings
WANG Xiu-jian, DU Xian-neng
2013, 34(5): 518-524. doi: 10.3879/j.issn.1000-0887.2013.05.010
Abstract(1005) PDF(1171)
Using homological methods, mainly prove that the class of the weak Gorenstein flat modules was projectively resolving if and only if it was closed under extensions. Furthermore, some properties of weak Gorenstein flat modules under the wGF-rings were also given. Which generalized the results of D.Bennis and so on.
Construction of Compatible Hydrodynamics Algorithms With the Preservation of Spherical Symmetry
LIN Zhi-wei, JIANG Shao-en
2013, 34(5): 525-534.
Abstract(1048) PDF(1217)
The problem of preserving the spherical symmetry of fluid flow in twodimensional cylindrical geometry was detailed studied. This problem called for cautious analysis and design of the entire hydrodynamics algorithms, which led to various methods. A programs was created, which based on the following schemes: utilizing the staggered Lagrangian algorithms; evolving the momentum by using the modified pressure gradient operators introduced by Caramana; advancing the internal energy compatibly; utilizing the edge-centered artificial viscosity; including the effects of the subzonal pressure forces; and ensuring the secondorder time accuracy by combining the predictor and corrector steps. The conservation of total energy was also investigated, the necessity of maintaining constant nodal masses was discussed, and the dissipativity of edge-centered artificial viscosity based on the compatible hydrodynamics algorithms was proved. In the end, the comparisons between numerical results and the known solutions demonstrated the correctness and robustness of the programs.
Simulations of the Multi-Medium Problem Pre-Process: PreGenGrid
WANG Rui-li, LIN Zhong, YAN Wei
2013, 34(5): 535-546. doi: 10.3879/j.issn.1000-0887.2013.05.012
Abstract(1159) PDF(920)
Main functions of a multi-medium problem pre-processor PreGenGrid was introduced. Including description of complex geometric regions, mesh generation of block area, data structure of the grid management, the seamless splicing technology of block meshes. Automatic mesh generation/automation patching of PreGenGrid was presented with emphases. Mesh examples were also provided. PreGenGrid is an ideal tool for computer aided in simulations of the multi-medium problem analysis in scientific computing.