Development of Computational Fluid Dynamics for Dispersed Open System

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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.