论文标题
用于凝固融化问题的混合水平集 /嵌入式边界方法
A hybrid level-set / embedded boundary method applied to solidification-melt problems
论文作者
论文摘要
在本文中，我们介绍了一种新颖的方式来代表随相变的两相流的界面。我们将级别的方法与笛卡尔嵌入式边界方法相结合，并利用这两者。这是获得数值策略的一部分，该策略依靠笛卡尔网格，允许模拟复杂边界，并可能改变拓扑，同时保留界面上梯度的高阶表示以及在界面上正确应用边界条件的能力。这导致了两流体保守的二阶数值方法。该方法正确解决Stefan问题的能力，具有和不具有各向异性的带有树突生长的能力，可以通过多种测试用例证明。最后，我们利用两流体表示形式来建模具有熔化边界的雷利 - 贝纳德不稳定性。
In this paper, we introduce a novel way to represent the interface for two-phase flows with phase change. We combine a level-set method with a Cartesian embedded boundary method and take advantage of both. This is part of an effort to obtain a numerical strategy relying on Cartesian grids allowing the simulation of complex boundaries with possible change of topology while retaining a high-order representation of the gradients on the interface and the capability of properly applying boundary conditions on the interface. This leads to a two-fluid conservative second-order numerical method. The ability of the method to correctly solve Stefan problems, onset dendrite growth with and without anisotropy is demonstrated through a variety of test cases. Finally, we take advantage of the two-fluid representation to model a Rayleigh--Bénard instability with a melting boundary.
