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  • 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 >

  • Open Access


    An Artificial Boundary Method for Burgers’ Equation in the Unbounded Domain

    Quan Zheng1,2, Lei Fan1, Xuezheng Li1

    CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.6, pp. 445-461, 2014, DOI:10.3970/cmes.2014.100.445

    Abstract In this paper, we construct a numerical method for one-dimensional Burgers’ equation in the unbounded domain by using artificial boundary conditions. The original problem is converted by Hopf-Cole transformation to the heat equation in the unbounded domain, the latter is reduced to an equivalent problem in a bounded computational domain by using two artificial integral boundary conditions, a finite difference method with discrete artificial boundary conditions is established by using the method of reduction of order for the last problem, and thereupon the numerical solution of Burgers’ equation is obtained. This artificial boundary method is proved and verified to be… More >

  • Open Access


    Numerical Solution of System of N–Coupled Nonlinear Schrödinger Equations via Two Variants of the Meshless Local Petrov–Galerkin (MLPG) Method

    M. Dehghan1, M. Abbaszadeh2, A. Mohebbi3

    CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.5, pp. 399-444, 2014, DOI:10.3970/cmes.2014.100.399

    Abstract In this paper three numerical techniques are proposed for solving the system of N-coupled nonlinear Schrödinger (CNLS) equations. Firstly, we obtain a time discrete scheme by approximating the first-order time derivative via the forward finite difference formula, then for obtaining a full discretization scheme, we use the Kansa’s approach to approximate the spatial derivatives via radial basis functions (RBFs) collocation methodology. We introduce the moving least squares (MLS) approximation and radial point interpolation method (RPIM) with their shape functions, separately. It should be noted that the shape functions of RPIM unlike the shape functions of the MLS approximation have kronecker… More >

  • Open Access


    Parallel Control-volume Method Based on Compact Local Integrated RBFs for the Solution of Fluid Flow Problems

    N. Pham-Sy1, C.-D. Tran1, N. Mai-Duy1, T. Tran-Cong1

    CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.5, pp. 363-397, 2014, DOI:10.3970/cmes.2014.100.363

    Abstract In this paper, a high performance computing method based on the Integrated Radial Basis Function (IRBF), Control Volume (CV) and Domain Decomposition technique for solving Partial Differential Equations is presented. The goal is to develop an efficient parallel algorithm based on the Compact Local IRBF method using the CV approach, especially for problems with non-rectangular domain. The results showed that the goal is achieved as the computational efficiency is quite significant. For the case of square lid driven cavity problem with Renoylds number 100, super-linear speed-up is also achieved. The parallel algorithm is implemented in the Matlab environment using Parallel… More >

  • Open Access


    Boundary Layer Effect in Regularized Meshless Method for Laplace Equation

    Weiwei Li1, Wen Chen1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.5, pp. 347-362, 2014, DOI:10.3970/cmes.2014.100.347

    Abstract This paper presents an efficient strategy for the accurate evaluation of near-boundary solutions in the regularized meshless method (RMM), also known as the boundary layer effect associated with the boundary element method. The RMM uses the double layer potentials as its interpolation basis function. When the field point is close to the boundary, the basis function will present nearly strongand hyper-singularities, respectively, for potentials and its derivative. This paper represents the first attempt to apply a nonlinear transformation, based on sinh function, to the accurate evaluation of nearly singular kernels associated with the RMM. The accuracy and efficiency of the… More >

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