  Melting and solidification processes are often affected by natural convection
of the liquid, posing a multi-physics problem involving fluid flow, convective
and diffusive heat transfer, and phase-change reactions. Enthalpy methods
formulate this convection-coupled phase-change problem on a single
computational domain. The governing equations can be solved accurately with a
monolithic approach using mixed finite elements and Newton's method.
Previously, the monolithic approach has relied on adaptive mesh refinement to
regularize local nonlinearities at phase interfaces. This contribution instead
separates mesh refinement from nonlinear problem regularization and provides a
continuation procedure which robustly obtains accurate solutions on the tested
2D uniform meshes. A flexible and extensible open source implementation is
provided. The code is formally verified to accurately solve the governing
equations in time and in 2D space, and convergence rates are shown. Two
benchmark simulations are presented in detail with comparison to experimental
data sets and corresponding results from the literature, one for the melting of
octadecane and another for the freezing of water. Sensitivities to key
numerical parameters are presented. For the case of freezing water, effective
reduction of numerical errors from these key parameters is successfully
demonstrated. Two more simulations are briefly presented, one for melting at a
higher Rayleigh number and one for melting gallium.
