Numerical simulation of moving boundary problem by modified Keller box method with boundary immobilisation technique

A modified Keller box (MKB) method is applied to the moving boundary problem (MBP) based on the boundary immobilisation technique. MBP is the modelling of the melting or solidification process. The mathematical importance of this problem is that the boundary of the domain is also unknown. The moving front position depends on time; hence this problem is inherently non-linear. Simulation time is used to evaluate the computational complexity of the schemes. The proposed scheme is compared to the existing schemes in the literature regarding the accuracy and simulation time. In both space and time, the proposed scheme has a second-order accuracy. For the known boundary, the constant boundary condition is taken and the proposed numerical algorithm is validated with the corresponding similarity solution. The MKB method provides good agreement with the similarity solution and also confirms that the computational rate of convergence of our scheme is two. This paper gives an idea of the MKB scheme for an MBP. This mathematical framework can be extended to 2D and 3D MBPs.