Flow with moving free surfaces is analyzed with an the Eulerian coordinate system. This study proposes a semi-implicit filling algorithm using VOF in which the PLIC (Piecewise Linear Interface Calculation) -type interface reconstruction method and the donor-acceptor-type front advancing scheme are adopted. Also, a new scheme using extrapolation of the stream function is proposed to find the velocity of the node that newly enters the computational domain. The effect of wall boundary conditions on the flow field and temperature field is examined by numerically solving a two-dimensional casting process.