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.
翻译:我们提出了一个战略,以解决相交相交的过渡阶段问题的数字解决方案,重点是固化和熔化;我们解决温度和流动场的长期问题;分阶段交换接口的位置以水平定制方法跟踪,这种方法要求了解界面热通量的不连续性;为了计算热通量跳跃,我们以幽细胞方法为基础,将其扩大到时空有限元素方法;这一技术不需要在当地丰富基础功能,例如延长的有限元素等方法,而且很容易在现有的有限元素代码中实施;提供了1D Stefan问题的核查案例和由液态驱动的裂变融化问题;此外,鉴于复杂的应用,我们展示了一个更精细的2D案例。