Home / Journals / CMES / Vol.70, No.3, 2010
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  • Open Access

    ARTICLE

    Galerkin/Collocation Methods Based on 1D-Integrated-RBFNs for Viscoelastic Flows

    D. Ho-Minh1, N. Mai-Duy1, T. Tran-Cong1
    CMES-Computer Modeling in Engineering & Sciences, Vol.70, No.3, pp. 217-252, 2010, DOI:10.3970/cmes.2010.070.217
    Abstract In this paper, one-dimensional integrated radial-basis-function networks (1D-IRBFNs) are introduced into the Galerkin and point-collocation formulations to simulate viscoelastic flows. The computational domain is represented by a Cartesian grid and IRBFNs, which are constructed through integration, are employed on each grid line to approximate the field variables including stresses in the streamfunction-vorticity formulation. Two types of fluid, namely Oldroyd-B and CEF models, are considered. The proposed methods are validated through the numerical simulation of several benchmark test problems including flows in a rectangular duct and in a corrugated tube. Numerical results show that accurate results are obtained using relatively-coarse grids. More >

  • Open Access

    ARTICLE

    Divergent Integrals in Elastostatics: Regularization in 3-D Case

    V.V. Zozulya1
    CMES-Computer Modeling in Engineering & Sciences, Vol.70, No.3, pp. 253-350, 2010, DOI:10.3970/cmes.2010.070.253
    Abstract In this article the divergent integrals, which arise when the boundary integral equation (BIE) methods are used for solution of the 3-D elastostatic problems is considered. The same approach for weakly singular, singular and hypersingular integral regularization is developed. The approach is based on theory of distribution and Green's theorems. This approach is applied for regularization of the divergent integrals over convex polygonal boundary elements (BE) in the case of piecewise constant approximation and over rectangular and triangular BE for piecewise linear approximation. The divergent integrals are transformed into the regular contour integrals that can be easily calculated analytically. Proposed… More >

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