M. Mohammadi¹, R. Mokhtari^2,3, 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 >

Lifeng Wang¹, Yunpeng Ma^1,2, 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 >

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 >

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 >

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 >

Shaohua Zhang^1,2, Pei Li¹, Yongteng Zhong¹, Jiawei Xiang^1,3

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 >

Lei Lu^1,2, Li-Hua Liu^3,4, 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 >

Abdul-Majid Wazwaz¹, R,olph Rach², Lazhar Bougoffa³, Jun-Sheng Duan^{4, 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 >

Hao Zuo^1,2, Zhi-Bo Yang^1,2,3, Xue-Feng Chen^1,2, Yong Xie⁴, Xing-Wu Zhang^1,2, 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 >

Lei Lu^1,2,3, 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 >