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A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform

A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform
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Year:    2011

Author:    A. Tadeu, C. S. Chen, J. Antόnio, Nuno Simões

Advances in Applied Mathematics and Mechanics, Vol. 3 (2011), Iss. 5 : pp. 572–585

Abstract

Fourier transform is applied to remove the time-dependent variable in the diffusion equation. Under non-harmonic initial conditions this gives rise to a non-homogeneous Helmholtz equation, which is solved by the method of fundamental solutions and the method of particular solutions. The particular solution of Helmholtz equation is available as shown in [4, 15]. The approximate solution in frequency domain is then inverted numerically using the inverse Fourier transform algorithm. Complex frequencies are used in order to avoid aliasing phenomena and to allow the computation of the static response. Two numerical examples are given to illustrate the effectiveness of the proposed approach for solving 2-D diffusion equations.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.10-m1039

Advances in Applied Mathematics and Mechanics, Vol. 3 (2011), Iss. 5 : pp. 572–585

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Transient heat transfer meshless methods method of particular solutions method of fundamental solutions frequency domain Fourier transform.

Author Details

A. Tadeu

C. S. Chen

J. Antόnio

Nuno Simões

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