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Numerical Analysis of a Model of Metal Solidification, 2D Case

机译：二维金属凝固模型的数值分析

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The work discusses numerical simulation of metal solidification. The difficulties of calculatibg such processes are that simulation is conducted at several scale levels simultaneously. At present experimental studies cover numerous aspects of metal solidification; however, there is no generalized concept of this process. The model applied in this study is based on the concept of solidified alloy in the form of a porous medium, where propagation of perturbations is described by the Biot equations. In order to describe nucleation, the modified Cahn—Hillard equation is applied. Previously a one-dimensional (ID) numerical model has been developed, its convergence has been demonstrated and a possibility of obtaining of various modes of solidification has been shown at modification of parameters. This work presents the 2D numerical model and examples of calculations. Since a multiscale approach requires high CPU resources, the 2D calculations are based on explicit and explicit-iterative algorithms which are efficiently implemented using a multiprocessor computer.
机译：这项工作讨论了金属凝固的数值模拟。计算这样的过程的困难在于同时在几个规模水平上进行模拟。目前的实验研究涵盖了金属凝固的许多方面。但是，此过程没有通用的概念。本研究中使用的模型基于多孔介质形式的凝固合金的概念，其中扰动的传播由Biot方程描述。为了描述成核作用，应用了改进的Cahn-Hillard方程。先前已经开发出一维（ID）数值模型，已经证明了其收敛性，并且已经显示了在修改参数时获得各种凝固模式的可能性。这项工作介绍了二维数值模型和计算示例。由于多尺度方法需要大量的CPU资源，因此2D计算基于显式和显式迭代算法，这些算法可使用多处理器计算机有效地实现。

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