CMES-Vol. 22, No. 3, 2007

Open Access

ARTICLE

A Meshless Local Petrov-Galerkin Method for Magnetic Diffusion in Non-magnetic Conductors
J.N. Johnson¹, J.M. Owen²
CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.3, pp. 165-188, 2007, DOI:10.3970/cmes.2007.022.165
Abstract In this paper, we propose a Meshless Local Petrov-Galerkin method for studying the diffusion of a magnetic field within a non-magnetic (μ = μ₀) conducting medium with non-homogeneous and anisotropic electrical resistivity. We derive a local weak form for the magnetic diffusion equation and discuss the effects of different trial/test functions and nodal spacings on its solution. We then demonstrate that the method produces convergent results for several relevant one-dimensional test problems for which solutions are known. This method has the potential to be combined with other mesh-free methods such as Smoothed Particle Hydrodynamics (SPH) to solve problems in resistive… More >

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Effect of Interface Modification on the Mechanical Behavior of Carbon Nanotube Reinforced Composites Using Parallel Molecular Dynamics Simulations
S. Namilae¹, U. Ch,ra², A Srinivasan³, N. Ch,ra⁴
CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.3, pp. 189-202, 2007, DOI:10.3970/cmes.2007.022.189
Abstract Molecular dynamics (MD) simulations play an important predictive role in understanding the behavior of nanoscale systems. In this paper, parallel MD simulations are used to understand the mechanical behavior of interfaces in CNT based composites. We present an algorithm for parallel implementation of MD simulations of carbon nanotube (CNT) based systems using reactive bond order potentials. We then use that algorithm to model the CNT-polymer interfaces with various levels of interaction as (a) described only by long range Van Der Waals interactions (b) chemically bonded with fixed matrix and (c) chemically bonded with matrix explicitly modeled. It is shown that… More >

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Lattice Boltzmann Method Simulation of Channel Flow with Square Pillars inside by the Field Synergy Principle
Cha’o-Kuang Chen¹, Shing-Cheng Chang¹, Szu-Yu Sun¹
CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.3, pp. 203-216, 2007, DOI:10.3970/cmes.2007.022.203
Abstract In this study, the channel flow is discussed by the LBM simulations. In the cases of channel with obstacles inside, the square pillars play the role of causing interruption within the fluid field, and hence change the direction of fluid flow. The recirculation region is formed behind the obstacles and influences the fluid passed through not only in the velocity field but also in the temperature field. Therefore, heat transfer is enhanced in local region.
The field synergy principle is applied in the research to demonstrate that the increased interruption within the fluid increases the synergistic level between the… More >

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Application of the MLPG to Thermo-Piezoelectricity
J. Sladek¹, V. Sladek¹, Ch. Zhang², P. Solek³
CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.3, pp. 217-234, 2007, DOI:10.3970/cmes.2007.022.217
Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of boundary value problems for coupled thermo-electro-mechanical fields. Transient dynamic governing equations are considered here. To eliminate the time-dependence in these equations, the Laplace-transform technique is applied. Material properties of piezoelectric materials are influenced by a thermal field. It is leading to an induced nonhomogeneity and the governing equations are more complicated than in a homogeneous counterpart. Two-dimensional analyzed domain is subdivided into small circular subdomains surrounding nodes randomly spread over the whole domain. A unit step function is used as the test functions in the… More >

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Perfectly matched layer for acoustic waveguide modeling --- benchmark calculations and perturbation analysis
Ya Yan Lu¹, Jianxin Zhu²
CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.3, pp. 235-248, 2007, DOI:10.3970/cmes.2007.022.235
Abstract The perfectly matched layer (PML) is a widely used technique for truncating unbounded domains in numerical simulations of wave propagation problems. In this paper, the PML technique is used with a standard one-way model to solve a benchmark problem for underwater acoustics modeling. Accurate solutions are obtained with a PML layer with a thickness of only a quarter of the wavelength. The effect of a PML is analyzed in a perturbation analysis for waveguides. More >

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