The melting of pure gallium in a rectangular cavity has been numerically investigated using the enthalpy-porosity approach for modeling combined convection-diffusion phase change. The major advantage of this technique is that it allows a fixed-grid solution of the coupled momentum and energy equations to be undertaken without resorting to variable transformations. In this work, a two-dimensional dynamic model is used and the influence of laminar natural-convection flow on the melting process is considered. Excellent agreement exists between the numerical predictions and experimental results available in the literature. The enthalpy-porosity approach has been found to converge rapidly, and is capable of producing accurate results for both the position and morphology of the melt front at different times with relatively modest computational requirements. These results may be taken to be a sound validation of this technique for modeling isothermal phase changes in metallurgical systems.

After a brief review of current source-based methods for modeling solidification phase change systems, a new source-based method for the treatment of latent heat evolution is presented. The essential feature of the proposed method is linearization of the discretized source term. This results in a robust and accurate computational method that can deal efficiently with a wide range of latent heat evolution mechanisms (i.e., liquid fraction temperature relationships). The proposed method is illustrated on application to a test problem in which various liquid fraction temperature relationships are employed.