CMES-Vol. 59, No. 2, 2010

Open Access

ARTICLE

Analytic Closed Solution for the Heat Conduction with Time Dependent Heat Convection Coefficient at One Boundary
Han Taw Chen¹, Shao Lun Sun¹, Hui Chen Huang¹, Sen Yung Lee^1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.2, pp. 107-126, 2010, DOI:10.3970/cmes.2010.059.107
Abstract A new solution method is proposed to develop the analytic closed form solution for the one dimensional heat conduction with one mixed type boundary condition and general time dependent heat convection coefficient for the first time. The solution method is the combination of an extension of the shifting function method developed by Lee and his colleagues and a series expansion. It is shown that the solution is simple and accurate. The convergence of the present analysis is very fast. One can find that when the dimensionless Fourier number is greater than 0.2, the error for More >

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ARTICLE

A Comparative Study of Global and Local Meshless Methods for Diffusion-Reaction Equation
Guangming Yao¹, Siraj-ul-Islam², Božidar Šarler²
CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.2, pp. 127-154, 2010, DOI:10.3970/cmes.2010.059.127
Abstract This paper focuses on the comparative study of global and local meshless methods based on collocation with radial basis functions for solving two dimensional initial boundary value diffusion-reaction problem with Dirichlet and Neumann boundary conditions. A similar study was performed for the boundary value problem with Laplace equation by Lee, Liu, and Fan (2003). In both global and local methods discussed, the time discretization is performed in explicit and implicit way and the multiquadric radial basis functions (RBFs) are used to interpolate diffusion-reaction variable and its spatial derivatives. Five and nine nodded sub-domains are used… More >

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Error Bounds forDiscrete Geometric Approach
Lorenzo Codecasa¹, Francesco Trevisan²
CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.2, pp. 155-180, 2010, DOI:10.3970/cmes.2010.059.155
Abstract Electromagnetic problems spatially discretized by the so called Discrete Geometric Approach are considered, where Discrete Counterparts of Constitutive Relations are discretized within an Energetic Approach. Pairs of oriented dual grids are considered in which the primal grid is composed of (oblique) parallelepipeds, (oblique) triangular prisms and tetrahedra and the dual grid is obtained according to the barycentric subdivision. The focus of the work is the evaluation of the constants bounding the approximation error of the electromagnetic field; the novelty is that such constants will be expressed in terms of the geometrical details of oriented dual More >

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A new incompressible Navier-Stokes solver combining Fourier pseudo-spectral and immersed boundary methods
F.P. Mariano¹, L.Q. Moreira¹, A. Silveira-Neto¹, C.B. da Silva², J.C.F. Pereira²
CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.2, pp. 181-216, 2010, DOI:10.3970/cmes.2010.059.181
Abstract A new numerical methodology combining Fourier pseudo-spectral and immersed boundary methods - IMERSPEC - is developed for fluid flow problems governed by the incompressible Navier-Stokes equations. The numerical algorithm consists in a classical Fourier pseudo-spectral methodology using the collocation method where wall boundary conditions are modelled by using an immersed boundary method (IBM). The performance of that new methodology is exemplified in two-dimensional numerical simulations of Green-Taylor decaying vortex, lid-driven cavity and flow over a square cylinder. The convergence rate, the accuracy, the influence of the Reynolds number and the external domain size are analyzed. More >

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