Abstract This paper deals with a two dimensional Stefan problem of solidification in arbitrary bounded domains. To realize this, the governing equations are transformed from a complex physical domain to a simpler computational domain using body-fitted coordinates and the corresponding transformed equations are solved using an alternating direction implicit (ADI) method. Stability analysis of the proposed ADI scheme, applied to the transformed equations, is discussed using von Neumann method. The developed scheme is then used to solve problems which are initially defined in some regular geometries like rectangular or circular but changes with time to some complex shapes. Comparisons with the existing schemes show that the developed scheme produced better solutions.

中文翻译：

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不规则几何中 Stefan 问题的基于 ADI 的贴体方法

摘要 本文处理任意有界域中凝固的二维Stefan 问题。为了实现这一点，使用体拟合坐标将控制方程从复杂的物理域转换为更简单的计算域，并使用交替方向隐式 (ADI) 方法求解相应的转换方程。使用冯诺依曼方法讨论了所提出的 ADI 方案应用于变换方程的稳定性分析。然后使用开发的方案来解决一些问题，这些问题最初定义为一些规则几何图形，如矩形或圆形，但随着时间的推移而改变为一些复杂的形状。与现有方案的比较表明，所开发的方案产生了更好的解决方案。