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A projection method for convection-dominated phase transitions

机译：对流主导相变的投影方法

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A simple model for solving convection/diffusion phase-transition problems is described. Pure substances are the focus of this article, but extensions to more complex temperature dependent phase-transitioning behavior are also addressed. The model uses a nondeforming, staggered Cartesian grid. A Boussinesq approximation is the driving force for natural convection, while the Poisson pressure-correction equation is solved with a conjugate gradient method. A simple marking method for liquid and solid cells is updated at every time step such that the pressure correction needs to be solved only in the domain where the substance is liquid. A projection method derived in this article is used to solve the thermal fields (i.e., solid fraction and temperature). A description of the Darcy source term for handling fluid flow in the solid region and a source-based method for solving the thermal fields are also presented; the latter is compared with the method derived in this article. Model validation is done by comparison with experimental results from a two-dimensional cavity convection/diffusion case with gallium. (C) 2018 Elsevier Inc. All rights reserved.
机译：描述了解决对流/扩散相变问题的简单模型。纯物质是本文的重点，但也涉及了对更复杂的温度相关相变行为的扩展。该模型使用非变形，交错的笛卡尔网格。 Boussinesq逼近是自然对流的驱动力，而泊松压力校正方程则用共轭梯度法求解。在每个时间步骤上都会更新用于液体和固体细胞的简单标记方法，以便仅在物质为液体的区域中需要解决压力校正问题。本文推导的投影方法用于求解热场（即，固体分数和温度）。还介绍了用于处理固体区域中流体流动的Darcy源项以及基于源的求解热场的方法。后者与本文得出的方法进行了比较。通过与带有镓的二维空腔对流/扩散情况下的实验结果进行比较来完成模型验证。 （C）2018 Elsevier Inc.保留所有权利。

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