采用延时修正法实施QUICK格式模拟提拉单晶体的生长

为了数值模拟提拉(又名Czochralski)法获得单晶体的生长过程,本文采用有限容积法离散控制方程,采用非均匀的交错网格避免不合理的振荡压力场,采用三阶精度QUICK (Quadratic Upwind Interpolation of Convective Kinematics)格式离散对流项,采用延时修正来实施QUICK格式获得满足主对角占优的代数方程组,采用SIMPLE(Semi-implicit Method for Pressure Linked Equations)算法耦合压力和速度场,给出了基于上述方法的方程、算法,并发展了程序,计算了Wheeler标准问题,计算结果与文献相当一致,同时本算法能模拟计算高葛拉晓夫数时的流动,显示出非均匀网格QUICK格式模拟晶体生长的优越性;另外本文将这一算法运用到单晶硅的数值模拟中,计算结果令人满意.

Numerical Simulation in Czochralski Crystal Growth by Deferred Correction QUICK Scheme

A finite volume method was used to study the melt flow in the Czochralski crystal growth process. A non-uniform staggered grid arrangement was used to avoid zigzag pressure field. A third order QUICK was used to discretize the convection term in the governing equations and it was implemented by using a deferred correction method to obtain diagonally dominant equations. The SIMPLE algorithm was employed to couple velocity and pressure field. The arithmetic was deduced by using the above method and the code developed was validated with application to the Wheeler s benchmark problems. Numerical calculations show that the present results agree quite well with available data in the literatures, and the present solver can simulate the flow with much higher Grashof number. In addition, this study shows the advantage of QUICK scheme with non-uniform grid for the simulation of crystal growth. In addition, the method was used to simulate the silicon melt growth and the result is satisfied.