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.

熔融和凝固过程通常受液体的自然对流影响，从而产生了涉及流体流动，对流和扩散传热以及相变反应的多物理场问题。焓方法在单个计算域上提出了对流耦合的相变问题。使用混合有限元和牛顿法的整体方法可以精确地求解控制方程。以前，单片方法依赖于自适应网格细化来规范相界面处的局部非线性。相反，此贡献将网格细化与非线性问题正则化分离开来，并提供了一种继续过程，可在测试的2D均匀网格上可靠地获得准确的解。提供了一种灵活且可扩展的开源实现。对该代码进行了正式验证，以准确地求解时间和二维空间中的控制方程，并显示了收敛速度。与实验数据集和文献中的相应结果进行了比较，详细介绍了两个基准模拟，一个模拟十八烷的熔融，另一个模拟水的冻结。介绍了对关键数字参数的敏感性。对于冷冻水，已成功证明了有效降低了这些关键参数的数值误差。简要介绍了另外两个模拟，一个模拟在较高的瑞利数下熔化，另一个在熔化镓上。与实验数据集和文献中的相应结果进行了比较，详细介绍了两个基准模拟，一个模拟十八烷的熔融，另一个模拟水的冻结。介绍了对关键数字参数的敏感性。对于冷冻水，已成功证明了有效降低了这些关键参数的数值误差。简要介绍了另外两个模拟，一个模拟在较高的瑞利数下熔化，另一个在熔化镓上。与实验数据集和文献中的相应结果进行了比较，详细介绍了两个基准模拟，一个模拟十八烷的熔融，另一个模拟水的冻结。介绍了对关键数字参数的敏感性。对于冷冻水，已成功证明了有效降低了这些关键参数的数值误差。简要介绍了另外两个模拟，一个模拟在较高的瑞利数下熔化，另一个在熔化镓上。