Classical numerical methods for solving solid–liquid phase change assume a constant density upon melting or solidification and are not efficient when applied to phase change with volume expansion or shrinkage. However, solid–liquid phase change is accompanied by a volume change and an appropriate numerical method must take this into account. Therefore, an efficient algorithm for solid–liquid phase change with a density change is presented. Its performance for a one-dimensional solidification problem and for the quasi two-dimensional melting of octadecane in a cubic cavity was tested. The new algorithm requires less than 1/9 of the iterations compared to the source based method in one dimension and less than 1/7 in two dimensions. Moreover, the new method is validated against PIV measurements from the literature. A conjugate heat transfer simulation, which includes parts of the experimental setup, shows that parasitic heat fluxes can significantly alter the shape of the phase front near the bottom wall.