CMES-Vol. 88, No. 4, 2012

Open Access

ARTICLE

Robust Numerical Scheme for Singularly Perturbed Parabolic Initial-Boundary-Value Problems on Equidistributed Mesh
Srinivasan Natesan¹, S. Gowrisankar²
CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.4, pp. 245-268, 2012, DOI:10.3970/cmes.2012.088.245
Abstract In this article, we propose a parameter-uniform computational technique to solve singularly perturbed parabolic initial-boundary-value problems exhibiting parabolic layers. The domain is discretized with a uniform mesh on the time direction and a nonuniform mesh obtained via equidistribution of a monitor function for the spatial variable. The numerical scheme consists of the implicit-Euler scheme for the time derivative and the classical central difference scheme for the spatial derivative. Truncation error, and stability analysis are carried out. Error estimates are derived, and numerical examples are presented. More >

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A New Optimal Scheme for Solving Nonlinear Heat Conduction Problems
Chih-Wen Chang^1,2, Chein-Shan Liu³
CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.4, pp. 269-292, 2012, DOI:10.3970/cmes.2012.088.269
Abstract In this article, we utilize an optimal vector driven algorithm (OVDA) to cope with the nonlinear heat conduction problems (HCPs). From this set of nonlinear ordinary differential equations, we propose a purely iterative scheme and the spatial-discretization of finite difference method for revealing the solution vector x, without having to invert the Jacobian matrix D. Furthermore, we introduce three new ideas of bifurcation, attracting set and optimal combination, which are restrained by two parameters g and a. Several numerical instances of nonlinear systems under noise are examined, finding that the OVDA has a fast convergence More >

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Prandtl Number Signature on Flow Patterns of Electrically Conducting Fluid in Square Enclosure
Ridha Djebali^1,2, Bernard Pateyron², Mohamed El Ganaoui³
CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.4, pp. 293-308, 2012, DOI:10.3970/cmes.2012.088.293
Abstract We present in this study a numerical investigation of unsteady two-dimensional natural convection of an electrically conducting fluid in a square cavity under an externally imposed magnetic field. A temperature gradient is applied between the two opposing side walls parallel to y-direction, while the floor and ceiling parallel to x-direction are adiabatic. The flow is characterized by the Rayleigh number Ra raged in 103-106, the Prandtl number Pr ranged in 0.01-10, the Hartman number Ha determined by the strength of the imposed magnetic field ranged in 0-100 and its tilting angle from x-axis ranging from… More >

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A Multi-Scale Computational Method Integrating Finite Element Method with Atomic Interactions of Materials
Bin Gu^1,2,3, L. C. Zhang², Weifeng Yuan¹, Youjun Ning¹
CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.4, pp. 309-324, 2012, DOI:10.3970/cmes.2012.088.309
Abstract Bridging the atomic and continuous analyses is an important aspect in multi-scale mechanics. This paper develops a computational method to integrate the atomic potential of a material with the finite element method. The novelty of this method is that strain energy is calculated from the atomic potential without the assumption in the Cauchy-Born rule that deformation in a virtual atomic cell is homogeneous. In this new method, the virtual atomic cell deformation is interpolated according to the continuum displacements associated with the shape functions. The applications of the method to single crystal Si and Ge More >

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