CMES-Vol. 32, No. 1, 2008

Open Access

ARTICLE

A New Shooting Method for Solving Boundary Layer Equations in Fluid Mechanics
Chein-Shan Liu¹, Chih-Wen Chang², Jiang-Ren Chang^2,3
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 More >

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ARTICLE

A Numerical Solution of 2D Buckley-Leverett Equation via Gradient Reproducing Kernel Particle Method
Hossein M. Shodja^1,2,3, Alireza Hashemian^1,4
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 More >

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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 >

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Segmentation and Simulation of Objects Represented in Images using Physical Principles
Patrícia C.T. Gonçalves^1,2, João Manuel R.S. Tavares^1,2, R.M. Natal Jorge^1,3
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… More >

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