We present a strategy for the numerical solution of convection-coupled phase-transition problems, with focus on solidification and melting. We solve for the temperature and flow fields over time. The position of the phase-change interface is tracked with a level-set method, which requires knowledge of the heat-flux discontinuity at the interface. In order to compute the heat-flux jump, we build upon the ghost-cell approach and extend it to the space-time finite element method. This technique does not require a local enrichment of the basis functions, such as methods like extended finite elements, and it can be easily implemented in already existing finite element codes. Verification cases for the 1D Stefan problem and the lid-driven cavity melting problem are provided. Furthermore, we show a more elaborate 2D case in view of complex applications.

中文翻译：

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基于水平集的时空有限元方法对凝固和熔化过程进行建模

我们提出了一种对流耦合相变问题数值解的策略，重点是凝固和熔化。我们解决随时间变化的温度和流场。相变界面的位置通过水平设置方法进行跟踪，该方法需要了解界面处的热通量不连续性。为了计算热通量跃迁，我们建立在幻影单元方法的基础上，并将其扩展为时空有限元方法。这项技术不需要局部扩展基本功能，例如扩展有限元之类的方法，并且可以很容易地在已经存在的有限元代码中实现。提供了关于一维Stefan问题和盖子驱动型腔熔化问题的验证案例。此外，鉴于复杂的应用程序，我们展示了更为详尽的2D案例。