Open AccessAn application of finite element method for a moving boundary problem
Author(s) -
E.N. Aksan,
Hatice Karabenli,
Alaattin Esen
Publication year - 2017
Publication title -
thermal science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.339
H-Index - 43
eISSN - 2334-7163
pISSN - 0354-9836
DOI - 10.2298/tsci170613268a
Subject(s) - stefan problem , finite element method , boundary knot method , method of fundamental solutions , boundary (topology) , boundary problem , singular boundary method , position (finance) , boundary value problem , mathematics , collocation (remote sensing) , numerical analysis , domain (mathematical analysis) , collocation method , mathematical analysis , boundary element method , computer science , physics , differential equation , ordinary differential equation , thermodynamics , finance , machine learning , economics
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 ( ) s t 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 0.0005 t ∆ = , it is also seen from the tables, the numerical solutions converge to exact solutions for the larger element numbers.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom