In this study, a developed model for non-isothermal phase transition with natural convection is proposed by using peridynamic differential operator (PDDO). The dimensionless governing equations of heat source approach and vorticity-stream function approach are reconstructed into the non-local integral form. The Euler forward difference is used for time integration. The application of the developed PDDO model extends to simulations involving pure phase transition, pure natural convection, and non-isothermal phase transition coupled with natural convection. The validity and accuracy of the developed non-isothermal phase transition model are verified by comparing the PDDO simulation results with results in published literature. This research provides a new alternative approach for simulating phase transition and convection problems.

中文翻译：

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使用近场动力学微分算子分析自然对流的非等温相变问题

在本研究中，利用近场动力学微分算子（PDDO）提出了一种自然对流非等温相变模型。将热源法和涡流函数法的无量纲控制方程重构为非局部积分形式。欧拉前向差分用于时间积分。所开发的PDDO模型的应用扩展到涉及纯相变、纯自然对流以及与自然对流耦合的非等温相变的模拟。通过将PDDO模拟结果与已发表文献的结果进行比较，验证了所开发的非等温相变模型的有效性和准确性。这项研究为模拟相变和对流问题提供了一种新的替代方法。