二维稳态晶体生长控制方程的数值解

Numerical solution of governing equations for two-dimension steady state crystal growth

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。

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.