Development of Computational Fluid Dynamics for Dispersed Open System

本文提出了一种用于不可压缩流体数值分析的高速高精度格式。Navier-Stokes方程的平流项是非线性的，因此很难对其进行精确分析。然后，在本格式中，将Navier-Stokes方程分为平流相和非平流相两部分。平流相用双二次元分析，非平流相用双线性元分析。但双二次元素的使用使系数矩阵的计算时间增加。为了解决这一问题，采用GSMAC-FEM的高速技术，在一点积分的基础上加入沙漏矩阵，计算出系数矩阵。为了验证离散del算子的有效性，本文对MCZ（Magnetic-field applied Czochralski method）熔体模型进行了分析，MCZ熔体模型是大规模数值模拟的重要模型之一。所施加的磁场是工业界最近注意到的CUSP磁场。计算了五种线圈位置不同的磁场模型。然后，详细研究了磁场的影响，并与Watanabe的实验结果进行了比较。

In this report, we propose a high speed and high accuracy scheme for the numerical analysis of incompressible fluid. The advection term of the Navier-Stokes equation is nonlinear, therefore it is difficult to analyze it accurately. Then, in the present scheme, the Navier-Stokes equation is divided into two parts of advection phase and non-advection phase. The advection phase is analyzed with biquadratic elements, on the other hand the non-advection phase is solved with bilinear elements. But use of the biquadratic elements makes the calculation time for the coefficient matrices increase. In order to solve this problem, the coefficient matrices are calculated with one point integration to which the hourglass matrices are added, following the high speed technique of GSMAC-FEM.. This scheme is verified by three models such as the rotating cone model and the forced-driven cavity flows.In the present paper, in order to make sure that the discrete del operator is useful we analyze the MCZ (Magnetic-field applied Czochralski method) melt which is one of the most important models for the large-scale simulations. The imposed magnetic field is the CUSP magnetic field recently remarked by the industrial world. We calculate the five models which have the different position of coil for the magnetic field. Then, this numerical results are investigated in details about the influence of the magnetic field and compared with the Watanabe's experimental results.