快速算法
(西北工业大学 凝固技术国家重点实验室,西安 710072)
摘 要: 提出了固熔体合金在枝晶凝固过程中的溶质再分配模型, 模型由扩散微分方程和溶质守恒方程组成, 使用Crank-Nicholson有限差分法和Trapezoid法则离散控制方程,导出了一个计算固相内溶质界面浓度的迭代公式, 在TDMA算法基础上, 仅用一步迭代, 就可以解出凝固过程中的溶质浓度场。用此算法分析了Al-4.5Cu和Al-1.5Cu-3Zn等合金的溶质再分配过程,通过与实验解析解的比较, 发现数值模型和算法是严密内洽的。
关键字: 数值模型;溶质再分配;算法
(State Key Laboratory for Solidification Process,
Northwestern Polytechnic University, Xi′an 710072, China)
Abstract:Solute redistribution is controlled by solute partition and solute diffusion during dendritic solidification of the solid solution alloy and is described by solute diffusion differential equation and species conserve equation. The Crank Nicholson finite difference scheme and the trapezoid law were used to solve these equations; a new iteration equation was derived to calculate the solute concentration at the solid and liquid interface. The solute concentration field during solidification was calculated on TDMA-based rapid algorithm. The solute redistribution of Al-4.5Cu and Al-1.5Cu-3Zn alloys was analyzed by the algorithm and compared with the results of analytical formula, and it is proved that the numerical model is efficient and consistent.
Key words: numerical model; solute redistribution; algorithm