Journal de mathématiques appliquées et computationnelles

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

Abstract

A. Karamanli and A. MuÄŸan

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.