Control volume methods have recently been developed for fluid flow and heat transfer on unstructured meshes. In this study, we extend these methods to implement the solution of natural-convection-dominated melting of gallium by a fixed-grid method. A simple, robust, and reliable explicit numerical method (MAC method) is applied for an unstructured triangular grid. This investigation also applies the implicit SIMPLER method for an unstructured triangular grid. Results obtained from the unstructured triangular grid correlate well with the structured mesh computations and experimental data. Also, the feasibility of applying the triangular grid to complex geometric problems is demonstrated by calculating two different triangular domains.