Home / Journals / CMES / Vol.19, No.1, 2007
Table of Content
  • Open Access

    ARTICLE

    A Solenoidal Initial Condition for the Numerical Solution of the Navier-Stokes Equations for Two-Phase Incompressible Flow

    F. Bierbrauer, S.-P. Zhu1
    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.1, pp. 1-22, 2007, DOI:10.3970/cmes.2007.019.001
    Abstract Recently the use of the one-field formulation in the numerical solution of the Navier-Stokes equations for two-phase incompressible flow has become a very attractive approach in CFD (computational fluid dynamics). While the presence of material discontinuities across fluid interfaces presents some difficulty, it is their combination with a non-solenoidal discontinuous initial velocity field, commonly occurring in the mathematical formulation, that has provided the greatest hindrance in the numerical solution. This paper presents three analytical solutions, the Bounded Creeping Flow, Solenoidal and Conserved Solenoidal Solutions, which are both continuous, incompressible, retain as much of the original mathematical formulation as possible and… More >

  • Open Access

    ARTICLE

    Adaptive Random Field Mesh Refinements in Stochastic Finite Element Reliability Analysis of Structures

    M. Manjuprasad1, C. S. Manohar2
    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.1, pp. 23-54, 2007, DOI:10.3970/cmes.2007.019.023
    Abstract A technique for adaptive random field refinement for stochastic finite element reliability analysis of structures is presented in this paper. Refinement indicator based on global importance measures are proposed and used for carrying out adaptive random field mesh refinements. Reliability index based error indicator is proposed and used for assessing the percentage error in the estimation of notional failure probability. Adaptive mesh refinement is carried out using hierarchical graded mesh obtained through bisection of elements. Spatially varying stochastic system parameters (such as Young's modulus and mass density) and load parameters are modeled in general as non-Gaussian random fields with prescribed… More >

  • Open Access

    ARTICLE

    Weight Function Shape Parameter Optimization in Meshless Methods for Non-uniform Grids

    J. Perko1, B. Šarler2
    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.1, pp. 55-68, 2007, DOI:10.3970/cmes.2007.019.055
    Abstract This work introduces a procedure for automated determination of weight function free parameters in moving least squares (MLS) based meshless methods for non-uniform grids. The meshless method used in present work is Diffuse Approximate Method (DAM). The DAM is structured in 2D with the one or two parameter Gaussian weigh function, 6 polynomial basis and 9 noded domain of influence. The procedure consists of three main elements. The first is definition of the reference quality function which measures the difference between the MLS approximation on non-uniform and hypothetic uniform node arrangements. The second is the construction of the object function… More >

  • Open Access

    ARTICLE

    A Novel Form of Reproducing Kernel Interpolation Method with Applications to Nonlinear Mechanics

    Amit Shaw1, D Roy2
    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.1, pp. 69-98, 2007, DOI:10.3970/cmes.2007.019.069
    Abstract A novel discretization strategy and derivative reproduction based on reproducing kernel (RK) particle approximations of functions are proposed. The proposed scheme is in the form of an RK interpolation that offers significant numerical advantages over a recent version of the strategy by Chen et al. (2003), wherein the authors added a set of primitive functions to the reproducing kernel (enrichment) functions. It was also required that the support size of the primitive function be less than the smallest distance between two successive grid points. Since the primitive function was required to vary from 0 to 1 within half of this… More >

  • Open Access

    ARTICLE

    A Meshless Regularized Integral Equation Method for Laplace Equation in Arbitrary Interior or Exterior Plane Domains

    Chein-Shan Liu 1
    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.1, pp. 99-110, 2007, DOI:10.3970/cmes.2007.019.099
    Abstract A new meshless regularized integral equation method (MRIEM) is developed to solve the interior and exterior Dirichlet problems for the two-dimensional Laplace equation, which consists of three parts: Fourier series expansion, the second kind Fredholm integral equation and an analytically regularized solution of the unknown boundary condition on an artificial circle. We find that the new method is powerful even for the problem with complex boundary shape and with random noise disturbing the boundary data. More >

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