快速算法
(西北工業(yè)大學(xué) 凝固技術(shù)國家重點(diǎn)實(shí)驗(yàn)室，西安 710072)
摘 要: 提出了固熔體合金在枝晶凝固過程中的溶質(zhì)再分配模型， 模型由擴(kuò)散微分方程和溶質(zhì)守恒方程組成， 使用Crank-Nicholson有限差分法和Trapezoid法則離散控制方程，導(dǎo)出了一個(gè)計(jì)算固相內(nèi)溶質(zhì)界面濃度的迭代公式， 在TDMA算法基礎(chǔ)上， 僅用一步迭代， 就可以解出凝固過程中的溶質(zhì)濃度場。用此算法分析了Al-4.5Cu和Al-1.5Cu-3Zn等合金的溶質(zhì)再分配過程，通過與實(shí)驗(yàn)解析解的比較， 發(fā)現(xiàn)數(shù)值模型和算法是嚴(yán)密內(nèi)洽的。
關(guān)鍵字: 數(shù)值模型;溶質(zhì)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
