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  • Open Access


    High-Performance 3D Hybrid/Mixed, and Simple 3D Voronoi Cell Finite Elements, for Macro- & Micro-mechanical Modeling of Solids, Without Using Multi-field Variational Principles

    P. L. Bishay1, S.N. Atluri1

    CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 41-98, 2012, DOI:10.3970/cmes.2012.084.041

    Abstract Higher-order two-dimensional as well as low and higher-order three-dimensional new Hybrid/Mixed (H/M) finite elements based on independently assumed displacement, and judiciously chosen strain fields, denoted by HMFEM-2, are developed here for applications in macro-mechanics. The idea of these new H/M finite elements is based on collocating the components of the independent strain field, with those derived from the independently assumed displacement fields at judiciously and cleverly chosen collocation points inside the element. This is unlike the other techniques used in older H/M finite elements where a two-field variational principle was used in order to enforce both equilibrium and compatibility conditions… More >

  • Open Access


    An Operator Splitting Approximation Combined With The SUPG Method For Transport Equations With Nonlinear Reaction Term

    O. Baysal1, G. Tanoglu2

    CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 27-40, 2012, DOI:10.3970/cmes.2012.084.027

    Abstract In this work, an operator splitting method is proposed in order to obtain a stable numerical solution for transport equation with non-linear reaction term. We split the transport equation into a reaction part and an advection diffusion part. The former one which becomes a nonlinear ordinary differential equation can be approximated by the simple higher order integrator or solved exactly. The later one is approximated by the Streamline-Upwind Petrov-Galerkin (SUPG) method combined with the generalized Euler time integration (θ-method). Numerical results that illustrate the good performance of this method are reported. More >

  • Open Access


    Implementation of a Parallel Dual Reciprocity Boundary Element Method for the Solution of Coupled Thermoelasticity and Thermoviscoelasticity Problems

    M. Koyuncu1, F. Y. Ikikat1, G. C. Icoz2, B. Baranoglu3, A. Yazici2

    CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 13-26, 2012, DOI:10.3970/cmes.2012.084.013

    Abstract A parallel dual reciprocity boundary element method solution to thermoelasticity and thermoviscoelasticity problems is proposed. The DR-BEM formulation is given in Fourier Transform Space where the Time Space solutions are obtained through inverse Fourier Transform. The parallellization of the code is achieved through solving each frequency at a distinct computational node. The implemented parallel code is tested on 64-core IBM blade servers and it is seen that a linear speed-up is achieved. More >

  • Open Access


    On the Determination of the Singular Sturm-Liouville Operator from Two Spectra

    Etibar S. Panakhov1, Murat Sat2

    CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 1-12, 2012, DOI:10.3970/cmes.2012.084.001

    Abstract In this paper an inverse problem by two given spectrum for a second-order differential operator with coulomb singularity of the type A/x in zero point ( here A is constant), is studied. It is well known that two spectrum {λn} and {µn} uniquely determine the potential function q(x) in the singular Sturm-Liouville equation defined on interval (0,π]. The aim of this paper is to prove the generalized degeneracy of the kernel K(x,t) . In particular, we obtain a new proof of the Hochstadt's theorem concerning the structure of the difference q~(x) - q(x). More >

  • Open Access


    Bernstein Polynomials Method for Fractional Convection-Diffusion Equation with Variable Coefficients

    Yiming Chen, Mingxu Yi, Chen Chen, Chunxiao Yu

    CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.6, pp. 639-654, 2012, DOI:10.3970/cmes.2012.083.639

    Abstract In this paper, Bernstein polynomials method is proposed for the numerical solution of a class of space-time fractional convection-diffusion equation with variable coefficients. This method combines the definition of fractional derivatives with some properties of Bernstein polynomials and are dispersed the coefficients efficaciously. The main characteristic behind this method is that the original problem is translated into a Sylvester equation. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Numerical examples show that the method is effective. More >

  • Open Access


    A Generalized Level Set-Navier Stokes Numerical Method for Predicting Thermo-Fluid Dynamics of Turbulent Free Surface

    Ashraf Balabel

    CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.6, pp. 599-638, 2012, DOI:10.3970/cmes.2012.083.599

    Abstract In the present paper, a new generalized level set numerical method based on the Fast Marching Method is developed for predicting the moving interface thermo-fluid dynamics in turbulent free surface flows. The numerical method is devoted to predict the turbulent interfacial dynamics resulting from either aerodynamic force or thermocapillary effects. The unsteady Reynolds averaged Navier-Stokes equations (RANS) and energy equation are coupled with the level set method and solved separately in each phase using the finite volume method on a non-staggered grid system. The application of the fast marching technique enables the fast as well as the accurate transport of… More >

  • Open Access


    Parallel Node-based Local Tetrahedral Mesh Generation

    Y.F. Nie, Y.Q. Li, L. Wang

    CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.6, pp. 575-598, 2012, DOI:10.3970/cmes.2012.083.575

    Abstract In this paper, we introduce the parallel Node-based Local FEM (NLFEM)-a novel version of FEM with natural parallel performances and adaptivity to various complex parallel environments. As a crucial part of 3D NLFEM, the Node-based Local Tetrahedron Mesh Generation (NLTMG) algorithm is presented, where guaranteeing the global conformity of local meshes is a strategy of ensuring the validity of the NLFEM and decoupling the NLFEM. In order to generate conforming local mesh, we search the neighbor nodes by the neighborhood of a corresponding multilevel bucket and then those nodes are Delaunay tetrahedralized by the TetGen. Accordingly, we prove that the… More >

  • Open Access


    Boundary Integral Computation of Elastic Water Resisting Key Strata under the Condition of Discontinuous Load

    Dan Ma, Xianbiao Mao, Chong Li, Feng Du

    CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.6, pp. 561-574, 2012, DOI:10.3970/cmes.2012.083.561

    Abstract Water resisting key strata (WRKS) is one of the most important structures in green coal mining engineering, which has the functions of water-preserved mining and disaster prevention of water inrush, while elastic WRKS is treated as one of the problems for elastic plates in this paper. The existing literatures on elastic plates have largely restricted to different engineering but minority in coal mining engineering. Based on the mechanical models of clamped circular plate with sub-uniform load and simply supported by a concentrated force for elastic WRKS, using the boundary integral equations which is obtained by the natural boundary reduction, this… More >

  • Open Access


    The Mode Relation for Open Acoustic Waveguide Terminated by PML with Varied Sound Speed

    Jianxin Zhu, Zengsi Chen, Zheqi Shen

    CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.5, pp. 547-560, 2012, DOI:10.3970/cmes.2012.083.547

    Abstract An acoustic waveguide with continuously varying sound speed is discussed in this paper. When the waveguide is open along the depth, the perfectly matched layer (PML) is used to terminate the infinite domain. Since the sound speed is gradually varied, the density is assumed as constant in each fluid layer. For this waveguide, it is shown that the mode relation is derived by using the differential transfer matrix method (DTMM). To solve leaky and PML modes, Newton's iteration is applied, and Chebyshev pseudospectral method is used for obtaining initial guesses. The solutions are with high accuracy. More >

  • Open Access


    Numerical Investigation on Dynamical Response of Aluminum Foam Subject to Hypervelocity Impact With Material Point Method

    Weiwei Gong, Yan Liu, Xiong Zhang, Honglei Ma

    CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.5, pp. 527-546, 2012, DOI:10.3970/cmes.2012.083.527

    Abstract Owing to its low density and good energy absorption capability, aluminum foam is an excellent protective material for spacecraft against debris impact. However, because of its complicated microstructure, it is very difficult to generate a FEM mesh accounting for the real microstructure of the alluminum foam. On the contrary, it is very easy to model three-dimensional problems with very complicated geometry with meshfree/meshless methods. Furthermore, the material point method has obvious advantages in modeling problems involving extreme large deformation problems like hypervelocity impact problem. In this paper, a three-dimensional material point model accounting for the real microsctructure of aluminum foam… More >

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