Home / Journals / CMES / Vol.32, No.1, 2008
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  • Open Access

    ARTICLE

    A New Shooting Method for Solving Boundary Layer Equations in Fluid Mechanics

    Chein-Shan Liu1, Chih-Wen Chang2, Jiang-Ren Chang2,3
    CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.1, pp. 1-16, 2008, DOI:10.3970/cmes.2008.032.001
    Abstract In this paper, we propose a new method to tackle of two famous boundary layer equations in fluid mechanics, namely, the Falkner-Skan and the Blasius equations. We can employ this method to find unknown initial conditions. The pivotal point is based on the erection of a one-step Lie group element$\mathbf {G}(T)$ and the formation of a generalized mid-point Lie group element$\mathbf {G}(r)$. Then, by imposing$\mathbf {G}(T) = \mathbf {G}(r)$ we can seek the missing initial conditions through a minimum discrepancy from the target in terms of a weighting factor$r \in (0, 1)$. Numerical examples are worked out to persuade that… More >

  • Open Access

    ARTICLE

    A Numerical Solution of 2D Buckley-Leverett Equation via Gradient Reproducing Kernel Particle Method

    Hossein M. Shodja1,2,3, Alireza Hashemian1,4
    CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.1, pp. 17-34, 2008, DOI:10.3970/cmes.2008.032.017
    Abstract Gradient reproducing kernel particle method (GRKPM) is a meshless technique which incorporates the first gradients of the function into the reproducing equation of RKPM. Therefore, in two-dimensional space GRKPM introduces three types of shape functions rather than one. The robustness of GRKPM's shape functions is established by reconstruction of a third-order polynomial. To enforce the essential boundary conditions (EBCs), GRKPM's shape functions are modified by transformation technique. By utilizing the modified shape functions, the weak form of the nonlinear evolutionary Buckley-Leverett (BL) equation is discretized in space, rendering a system of nonlinear ordinary differential equations (ODEs). Subsequently, Gear's method is… More >

  • Open Access

    ARTICLE

    Fast Parallel Finite Element Approximate Inverses

    G.A. Gravvanis, K.M. Giannoutakis1
    CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.1, pp. 35-44, 2008, DOI:10.3970/cmes.2008.032.035
    Abstract A new parallel normalized optimized approximate inverse algorithm, based on the concept of the ``fish bone'' computational approach with cyclic distribution of the processors satisfying an antidiagonal data dependency, for computing classes of explicit approximate inverses, is introduced for symmetric multiprocessor systems. The parallel normalized explicit approximate inverses are used in conjunction with parallel normalized explicit preconditioned conjugate gradient square schemes, for the efficient solution of finite element sparse linear systems. The parallel design and implementation issues of the new proposed algorithms are discussed and the parallel performance is presented, using OpenMP. More >

  • Open Access

    ARTICLE

    Segmentation and Simulation of Objects Represented in Images using Physical Principles

    Patrícia C.T. Gonçalves1,2, João Manuel R.S. Tavares1,2, R.M. Natal Jorge1,3
    CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.1, pp. 45-56, 2008, DOI:10.3970/cmes.2008.032.045
    Abstract The main goals of the present work are to automatically extract the contour of an object and to simulate its deformation using a physical approach. In this work, to segment an object represented in an image, an initial contour is manually defined for it that will then automatically evolve until it reaches the border of the desired object. In this approach, the contour is modelled by a physical formulation using the finite element method, and its temporal evolution to the desired final contour is driven by internal and external forces. The internal forces are defined by the intrinsic characteristics of… More >

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