A second order accurate fixed-grid method for multi-dimensional Stefan problem with moving phase change materials

Abstract

This paper proposes a front-tracking fixed grid method for solving Stefan problem with moving phase change materials in any arbitrary (irregular) bounded domains. To achieve this objective, the governing partial differential equations are transformed, using a curvilinear coordinate transformation, in to a fixed rectangular domain, at each time level and an alternate direction implicit (ADI) scheme is used to solve the resultant differential system. The proposed scheme is consistent, unconditionally stable and also produces second-order accurate results. Many numerical experiments are conducted, in both one and two phase environments, to validate the proposed method. All these validations confirmed the theoretical accuracy of the produced results which are presented in the form of error graphs and tables in each case. Importance is given to understand the influence of the physical parameters like Peclet number, Stefan number, material velocity, latent heat, and thermal conductivity, etc., on the rate of change of phase and observed a continuous enhancement of the same with in the chosen range of the parameters. Also noticed a faster movement of the interface with the increase in these parameters in the direction of melting or freezing.