Numerical solutions for a Stefan problem

Year 2016, Volume: 4 Issue: 4, 175 - 187, 31.12.2016

Hatice Karabenli Alaattin Esen E.nesligul Aksan

Abstract

The initial version of a Stefan problem is the melting
of a semi-infinite sheet of ice. This problem is described by a parabolic
partial differential equation along with two boundary conditions on the moving
boundary which are used to determine the boundary itself and complete the
solution of the differential equation. In this paper firstly, we use variable
space grid method, boundary immobilisation method and isotherm migration method
to get rid of the trouble of the Stefan problem. Then, collocation finite
element method based on cubic B-spline bases functions is applied to model
problem. The numerical schemes of finite element methods provide a good
numerical approximation for the model problem. The numerical results show that
the present results are in good agreement with the exact ones.

Keywords

Stefan problems, variable space grid method, boundary immobilisation method, isotherm migration method

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