THERMAL SCIENCE

International Scientific Journal

Emine Nesligul Aksan

,

Hatice Karabenli

,

Alaattin Esen

AN APPLICATION OF FINITE ELEMENT METHOD FOR A MOVING BOUNDARY PROBLEM

ABSTRACT
The Stefan problems called as moving boundary problems are defined by the heat equation on the domain 0 < x < s(t). In these problems, the position of moving boundary is determined as part of the solution. As a result, they are non-linear problems and thus have limited analytical solutions. In this study, we are going to consider a Stefan problem described as solidification problem. After using variable space grid method and boundary immobilization method, collocation finite element method is applied to the model problem. The numerical solutions obtained for the position of moving boundary are compared with the exact ones and the other numerical solutions existing in the literature. The newly obtained numerical results are more accurate than the others for the time step Δt = 0.0005, it is also seen from the tables, the numerical solutions converge to exact solutions for the larger element numbers.
KEYWORDS
variable space grid method, Boundary Immobilization Method, Collocation Finite Element Method, Cubic B-Spline Basis Functions
PAPER SUBMITTED: 2017-06-13
PAPER REVISED: 2017-11-14
PAPER ACCEPTED: 2017-11-18
PUBLISHED ONLINE: 2018-01-07
DOI REFERENCE: https://doi.org/10.2298/TSCI170613268A
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Supplement 1, PAGES [S25 - S32]
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An application of finite element method for a moving boundary problem

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence