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  • Open Access


    A Meshless Method for Solving the 2D Brusselator Reaction-Diffusion System

    M. Mohammadi1, R. Mokhtari2,3, R. Schaback4

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.2, pp. 113-138, 2014, DOI:10.3970/cmes.2014.101.113

    Abstract In this paper, the two-dimensional (2D) Brusselator reaction-diffusion system is simulated numerically by the method of lines. The proposed method is implemented as a meshless method based on spatial trial functions in the reproducing kernel Hilbert spaces. For efficiency and stability reasons, we use the Newton basis introduced recently by Müller and Schaback. The method is shown to work in all interesting situations described by Hopf bifurcations and Turing patterns. More >

  • Open Access


    Legendre Polynomials Method for Solving a Class of Variable Order Fractional Differential Equation

    Lifeng Wang1, Yunpeng Ma1,2, Yongqiang Yang1

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.2, pp. 97-111, 2014, DOI:10.3970/cmes.2014.101.097

    Abstract In this paper, a numerical method based on the Legendre polynomials is presented for a class of variable order fractional differential equation. We adopt the Coimbra variable order fractional operator, which can be viewed as a Caputo-type definition. Three different kinds of operational matrixes with Legendre polynomials are derived. A truncated the Legendre polynomials series together with the products of several dependent matrixes are utilized to reduce the variable order fractional differential equation to a system of algebraic equations. The solution of this system gives the approximation solution for the truncated limited n. An error analysis technique is also given.… More >

  • Open Access


    Coupled ABC and Spline Collocation Approach for a Class of Nonlinear Boundary Value Problems over Semi-Infinite Domains

    S.A. Khuri1, A. Sayfy1

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.2, pp. 81-96, 2014, DOI:10.3970/cmes.2014.101.081

    Abstract In this article, we introduce a numerical scheme to solve a class of nonlinear two-point BVPs on a semi-infinite domain that arise in engineering applications and the physical sciences. The strategy is based on replacing the boundary condition at infinity by an asymptotic boundary condition (ABC) specified over a finite interval that approaches the given value at infinity. Then, the problem complimented with the resulting ABC is solved using a fourth order spline collocation approach constructed over uniform meshes on the truncated domain. A number of test examples are considered to confirm the accuracy, efficient treatment of the boundary condition… More >

  • Open Access


    CFD and Experimental Investigations of Drag Force on Spherical Leak Detector in Pipe Flows at High Reynolds Number

    ShiXu Guo1, Shili Chen1, Xinjing Huang1, Yu Zhang1, Shijiu Jin1

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.1, pp. 59-80, 2014, DOI:10.3970/cmes.2014.101.059

    Abstract Spherical leak detectors can detect very tiny leakage in pipelines and have low risk of blockage. In this paper the passing ability of the detector in the vertical segment of a pipe was studied using CFD simulations and experiments. The Reynolds number for the sphere exceeds 104 at the economical velocity range for oil pipelines, and there were few researches related to the hydrodynamic force on the sphere by the pipe flow at high Reynolds number. For sphere with different sizes and density, and at different flow rates, more than 100 3-D steady numerical simulations were carried out. The simulation… More >

  • Open Access


    A Fully Discrete SCNFVE Formulation for the Non-stationary Navier-Stokes Equations

    Zhendong Luo1, Fei Teng2

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.1, pp. 33-58, 2014, DOI:10.3970/cmes.2014.101.033

    Abstract A semi-discrete Crank-Nicolson (CN) formulation about time and a fully discrete stabilized CN finite volume element (SCNFVE) formulation based on two local Gauss integrals and parameter-free with the second-order time accuracy are established for the non-stationary Navier-Stokes equations. The error estimates of the semi-discrete and fully discrete SCNFVE solutions are derived. Some numerical experiments are presented to illustrate that the fully discrete SCNFVE formulation possesses more advantages than its stabilized finite volume element formulation with the first-order time accuracy, thus validating that the fully discrete SCNFVE formulation is feasible and efficient for finding the numerical solutions of the non-stationary Navier-Stokes… More >

  • Open Access


    Structural Topology Optimization Based on the Level Set Method Using COMSOL

    Shaohua Zhang1,2, Pei Li1, Yongteng Zhong1, Jiawei Xiang1,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.1, pp. 17-31, 2014, DOI:10.3970/cmes.2014.101.017

    Abstract In order to obtain smooth boundary and improve computational efficiency, a new topology optimization scheme based on the level set method is presented. Using the level set function as design variable and the volume ratio of the solid material as volume constraint, respectively, this scheme can easily implement compliance minimization structure topology optimization in associated with the reaction-diffusion equation in commercial software COMSOL. Compared with the results of solid isotropic material with penalization (SIMP) and traditional level set method, this scheme obtained a smooth geometry boundary. In the present computational scheme, the computational cost could be enormously saved without solving… More >

  • Open Access


    Investigation of Squeezing Unsteady Nanofluid Flow Using the Modified Decomposition Method

    Lei Lu1,2, Li-Hua Liu3,4, Xiao-Xiao Li1

    CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.1, pp. 1-15, 2014, DOI:10.3970/cmes.2014.101.001

    Abstract In this paper, we use the modified decomposition method (MDM) to solve the unsteady flow of a nanofluid squeezing between two parallel equations. Copper as nanoparticle with water as its base fluid has considered. The effective thermal conductivity and viscosity of nanofluid are calculated by the Maxwell- Garnetts (MG) and Brinkman models, respectively. The effects of the squeeze number, the nanofluid volume fraction, Eckert number, δ on Nusselt number and the Prandtl number are investigated. The figures and tables clearly show high accuracy of the method to solve the unsteady flow. More >

  • Open Access


    Solving the Lane–Emden–Fowler Type Equations of Higher Orders by the Adomian Decomposition Method

    Abdul-Majid Wazwaz1, R,olph Rach2, Lazhar Bougoffa3, Jun-Sheng Duan4, 5

    CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.6, pp. 507-529, 2014, DOI:10.3970/cmes.2014.100.507

    Abstract In this paper, we construct the Lane–Emden–Fowler type equations of higher orders. We study the linear and the nonlinear Lane–Emden–Fowler type equations of the third and fourth orders, where other forms can be treated in a similar manner. We use the systematic Adomian decomposition method to handle these types of equations with specified initial conditions. We confirm that the Adomian decomposition method provides an efficient algorithm for exact and approximate analytic solutions of these equations. We corroborate this study by investigating several numerical examples that emphasize initial value problems. More >

  • Open Access


    Static, Free Vibration and Buckling Analysis of Functionally Graded Beam via B-spline Wavelet on the Interval and Timoshenko Beam Theory

    Hao Zuo1,2, Zhi-Bo Yang1,2,3, Xue-Feng Chen1,2, Yong Xie4, Xing-Wu Zhang1,2, Yue Liu5

    CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.6, pp. 477-506, 2014, DOI:10.3970/cmes.2014.100.477

    Abstract The application of B-spline wavelet on the interval (BSWI) finite element method for static, free vibration and buckling analysis in functionally graded (FG) beam is presented in this paper. The functionally graded material (FGM) is a new type of heterogeneous composite material with material properties varying continuously throughout the thickness direction according to power law form in terms of volume fraction of material constituents. Different from polynomial interpolation used in traditional finite element method, the scaling functions of BSWI are employed to form the shape functions and construct wavelet-based elements. Timoshenko beam theory and Hamilton’s principle are adopted to formulate… More >

  • Open Access


    Solution of Two-Dimensional Viscous Flow in a Rectangular Domain by the Modified Decomposition Method

    Lei Lu1,2,3, Jun-Sheng Duan2, Long-Zhen Fan1

    CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.6, pp. 463-475, 2014, DOI:10.3970/cmes.2014.100.463

    Abstract In this paper, the modified decomposition method (MDM) for solving the nonlinear two-dimensional viscous flow equations is presented. This study investigates the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions. We first transform the original two-dimensional viscous flow problem into an equivalent fourth-order boundary value problem (BVP), then solve the problem by the MDM. The figures and tables clearly show high accuracy of the method to solve two-dimensional viscous flow. More >

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