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Mathematical and numerical model of solidification process of pure metals

机译：纯金属凝固过程的数学和数值模型

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This paper concerns the mathematical and numerical modeling of solidification process of pure metals. Such process takes place without development of "mushy zone", which very often occurs during solidification of alloys. The model is based on the finite element method (FEM) and takes into account the existence of a sharp solidification front which moves according to time. The paper discusses how to include the conditions of continuity on the moving interface as well as the technique of front tracking based on the level set method (LSM). The paper also presents the results of computer simulations of the solidification process of pure copper. Two in-home solvers for one- and two-dimensional problems were built. Both of them are based on FEM. The correctness of the front tracking technique was checked by comparing the results obtained from 2D simulation to 1D simulation. Furthermore, the final calculation process was done for the two-dimensional area at different temperatures on the boundaries to demonstrate the effectiveness of the solver for a complex shape of the solidification front.
机译：本文涉及纯金属凝固过程的数学和数值模型。这样的过程在没有“糊状区”的发展的情况下发生，该“糊状区”在合金的固化过程中经常发生。该模型基于有限元方法（FEM），并考虑了随时间变化的尖锐凝固前沿的存在。本文讨论了如何在移动界面上包含连续性条件，以及基于水平集方法（LSM）的前端跟踪技术。本文还介绍了纯铜凝固过程的计算机模拟结果。建立了两个针对一维和二维问题的家庭求解器。它们都基于FEM。通过比较从2D模拟获得的结果和1D模拟获得的结果，检查了正面跟踪技术的正确性。此外，在边界上不同温度下对二维区域进行了最终计算过程，以证明求解器对于复杂形状的凝固前沿的有效性。

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