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.
Highlights
The classical Stefan problem is the name given to an initial –boundary value problem, which involves both fixed and moving boundaries
In a previous article [2], the numerical solution for the free boundary problems has been investigated through the finite difference method (FDM) and the minimax approach
We consider the numerical solution for a two –sided Stefan problem where the free boundary depends on time only
Summary
The classical Stefan problem is the name given to an initial –boundary value problem, which involves both fixed and moving boundaries. Stefan direct problems are boundary value problems for parabolic heat equations in regions with unknown and moving boundaries, which requires determining the temperature [1]. We consider the numerical solution for a two –sided Stefan problem where the free boundary depends on time only. This problem is solved by FDM with Crank-Nicolson scheme. Where the continuous functions ( ) ( ) and ( ) are given This model has been investigated theoretically [7] and no numerical solution was obtained. The problem in fixed domain has the following form which will be solved numerically using a finite-difference scheme
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
