| 二维稳态晶体生长控制方程的数值解 |
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| 引用本文： | 廖福成,陶娟,刘贺平.二维稳态晶体生长控制方程的数值解[J].北京科技大学学报,2005,27(5):560-563. |
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| 作者姓名： | 廖福成 陶娟 刘贺平 |
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| 作者单位： | [1]北京科技大学应用科学学院,北京100083 [2]北京科技大学信息工程学院,北京100083 |
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| 基金项目： | 国家重点基础研究发展计划(973计划) |
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| 摘 要： | 分析了在均匀流场的作用下,金属凝固过程中晶体生长浓度的二维稳态方程的边值问题.运用有限差分法将微分方程数值离散化为线性代数方程组.用初等变换法将该代数方程组分解为多个方程组进行处理,提高了计算效率.模拟结果揭示了在均匀流场作用下,沿枝晶生长的方向,晶体生长的浓度呈现振荡衰减的本质特征
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| 关 键 词： | 晶体生长 偏微分方程 边值问题 数值解 二维稳态 晶体生长 控制方程 数值解 crystal growth steady state equations solution 特征 衰减 振荡 生长浓度 方向 枝晶生长 模拟结果 计算效率 处理 线性代数方程组 分解 初等变换法 |
| 收稿时间： | 10 27 2004 12:00AM |
| 修稿时间： | 03 18 2005 12:00AM |
Numerical solution of governing equations for two-dimension steady state crystal growth |
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| LIAO Fucheng, TAO Juan, LIU Heping.Numerical solution of governing equations for two-dimension steady state crystal growth[J].Journal of University of Science and Technology Beijing,2005,27(5):560-563. |
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| Authors: | LIAO Fucheng TAO Juan LIU Heping |
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| Institution: | 1. Applied Science School, University of Science and Technology Beijing, Beijing 100083, China; 2. Information Engineering School, University of Science and Technology Beijing, Beijing 100083, China |
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| Abstract: | A boundary value problem of governing equations for the concentration of crystal growth is solved in the two-dimension steady state considering the effect of uniform convection field. The differential equation is numerically discretized into a system of linear algebraic equations by using the finite difference method. In order to improve computational efficiency, the system of linear algebraic equations is decomposed to several sub-systems. The result of numerical simulation shows that the concentration of crystal growth in steady state presents oscillating attenuation along the direction of dendrite growth in the action of uniform convection field. |
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| Keywords: | crystal growth partial differential equation boundary value problem numerical solution |
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