Numerical Solution for Two-Sided Stefan Problem

  • Zahraa Adil Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
  • M.S. Hussein Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Keywords: Free boundary, Heat equation, FDM, Crank-Nicolson scheme

Abstract

     In this paper, we consider a two-phase Stefan problem in one-dimensional space for parabolic heat equation with non-homogenous Dirichlet boundary condition. This problem contains a free boundary depending on time. Therefore, the shape of the problem is changing with time. To overcome this issue, we use a simple transformation to convert the free-boundary problem to a fixed-boundary problem. However, this transformation yields a complex and nonlinear parabolic equation. The resulting equation is solved by the finite difference method with Crank-Nicolson scheme which is unconditionally stable and second-order of accuracy in space and time. The numerical results show an excellent accuracy and stable solutions for two test examples.

Published
2020-02-28
How to Cite
Adil , Z., & Hussein, M. (2020). Numerical Solution for Two-Sided Stefan Problem. Iraqi Journal of Science, 61(2), 444-452. https://doi.org/10.24996/ijs.2020.61.2.24
Section
Mathematics