Computer simulations of phase change processes are of high importance in research and industry. The phase change of a material from solid to liquid and vice versa is commonplace in many technical applications from metal production to latent heat thermal energy storage. As for computer modelling, most investigators and engineers use well-known interface capturing methods because of their simplicity and straightforward implementation. However, these methods often suffer from lower computational accuracy. The paper investigates the use of the front tracking method which utilizes explicit tracking of the interface between the phases. The assessment of the computational accuracy shows that the front tracking method is about two orders of magnitude more accurate than interface capturing methods. The acceleration by means of the graphics processing units (GPUs) was utilized to enhance the computational efficiency of the front tracking method. The results demonstrate that the front tracking method and its GPU-based acceleration represent a powerful tool for fast and accurate modelling of phase change processes. (C) 2018 Elsevier Ltd. All rights reserved.