Abstract The paper deals with the issue of particle growth in a two-component alloy. The particle is formed from chemical reaction products that occur at the phase boundary. A generalized mathematical model of particle growth includes diffusion equations, mass transfer equations in the boundary layer, and equations characterizing a change in the growing particle radius. The paper proposes an approach that reduces issues to the system of PDEs and ODE that describes the state of growing particle. This approach provides a basis for developing a numerical method for calculating the growing particle radius as a function of time, based on the obtained equations. The computational scheme involves the finite-difference analogues of equations with an additional regularizing functional that ensure method stability with respect to accumulated computational error. In order to verify reliability of the proposed computational scheme and to obtain experimental error estimates of numerical solutions, computational experiments were carried out. In the experiments, the growing particle radius is determined with respect to the time via the proposed method. Also, comparative analysis of the calculated radius with test values was carried out and experimental estimates of deviations of the calculated radius from the test functions were obtained. The experiment results presented in the work indicate sufficient accuracy of the developed numerical method.

中文翻译：

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确定双组分合金中粒子生长动力学的方法

摘要 本文讨论了双组分合金中的颗粒生长问题。粒子由发生在相界处的化学反应产物形成。粒子生长的广义数学模型包括扩散方程、边界层中的传质方程以及表征粒子生长半径变化的方程。该论文提出了一种方法，可以减少描述粒子生长状态的 PDE 和 ODE 系统的问题。该方法为基于获得的方程开发用于计算作为时间函数的增长粒子半径的数值方法提供了基础。计算方案涉及方程的有限差分类似物，具有额外的正则化函数，可确保方法相对于累积计算误差的稳定性。为了验证所提出的计算方案的可靠性并获得数值解的实验误差估计，进行了计算实验。在实验中，通过所提出的方法确定相对于时间的增长粒子半径。此外，还进行了计算半径与测试值的比较分析，并获得了计算半径与测试函数偏差的实验估计。工作中提出的实验结果表明所开发的数值方法具有足够的准确性。为了验证所提出的计算方案的可靠性并获得数值解的实验误差估计，进行了计算实验。在实验中，通过所提出的方法确定相对于时间的增长粒子半径。此外，还进行了计算半径与测试值的比较分析，并获得了计算半径与测试函数偏差的实验估计。工作中提出的实验结果表明所开发的数值方法具有足够的准确性。为了验证所提出的计算方案的可靠性并获得数值解的实验误差估计，进行了计算实验。在实验中，通过所提出的方法确定相对于时间的增长粒子半径。此外，还进行了计算半径与测试值的比较分析，并获得了计算半径与测试函数偏差的实验估计。工作中提出的实验结果表明，所开发的数值方法具有足够的准确性。对计算半径与测试值进行了比较分析，并获得了计算半径与测试函数偏差的实验估计。工作中提出的实验结果表明所开发的数值方法具有足够的准确性。对计算半径与测试值进行了比较分析，并获得了计算半径与测试函数偏差的实验估计。工作中提出的实验结果表明所开发的数值方法具有足够的准确性。