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

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.