焓形式对流耦合相变的混合有限元：开放式软件验证并应用于2D基准
Mixed finite elements for convection-coupled phase-change in enthalpy form: Open software verified and applied to 2D benchmarks
摘要：
熔化和凝固过程通常受到液体自然对流的影响，这是一个涉及流体流动、对流和扩散传热以及相变反应的多物理问题。焓方法制定了一个单一的计算域上的对流耦合相变问题。采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。在此之前，单片方法依赖于自适应网格细化来调整相界面处的局部非线性。这一贡献，而不是分离网格细化非线性问题的正则化，并提供了一个连续的过程，鲁棒地获得准确的解决方案，在测试的二维均匀网格。提供了一个灵活的和可扩展的开源实现。该代码被正式验证，以准确地解决在时间和二维空间的控制方程，并显示收敛速度。两个基准模拟详细比较实验数据集和相应的结果从文献中，一个为十八烷的熔化和另一个为水的冻结。关键数值参数的敏感性。对于冻结水的情况下，有效地减少这些关键参数的数值误差成功地证明。另外两个模拟简要介绍，一个熔融在较高的瑞利数和熔融镓。
英文摘要：
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.
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