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ISSN: 2168-9679

Journal of Applied & Computational Mathematics
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Research Article

Solutions of Two-Dimensional Heat Transfer Problems by Using Symmetric Smoothed Particle Hydrodynamics Method

A. Karamanli* and A. Mugan

Istanbul Technical University, Faculty of Mechanical Engineering, Gumussuyu 34437, Istanbul, Turkey

*Corresponding Author:
A. Karamanli
Istanbul Technical University
Faculty of Mechanical Engineering
Gumussuyu 34437, Istanbul, Turkey
Tel: (+90) 535 39 92 33
Fax: (+90) 212 249 51 97
E-mail: [email protected]

Received Date: May 19, 2012; Accepted Date: June 14, 2012; Published Date: June 17, 2012

Citation: Karamanli A, Mugan A (2012) Solutions of Two-Dimensional Heat Transfer Problems by Using Symmetric Smoothed Particle Hydrodynamics Method. J Appl Computat Math 1:112. doi: 10.4172/2168-9679.1000112

Copyright: © 2012 Karamanli A, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Abstract

The symmetric smoothed particle hydrodynamics (SSPH) method is used to generate the basis functions to solve 2D homogeneous and non-homogeneous steady-state heat transfer problems. The SSPH basis functions together with the collocation method (i.e, the strong formulation of the problem) are used to solve sample problems. Comparisons are made with the results obtained by using different weight functions and particle numbers. The error norms for three sample problems are computed by the use of two different kernel functions such as the revised Gauss function and revised super Gauss function, among which the revised super Gauss function yields the smallest error norm. It is observed that the SSPH method yields large errors for non-homogenous problems, especially if the forcing term is not smooth.

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