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In this paper, direct numerical simulations are presented for solidification with the effects of density difference between the solid and liquid phases. A front-tracking method is used. The solidification front, i.e. the solid-liquid interface separating solid and liquid, is represented by connected elements that move on a rectangular and stationary grid. The Navier-Stokes equations are solved by a projection method on the entire domain including the solid phase. An indicator function reconstructed from the front information is used to set the velocities in the solid phase to zero, and thus to enforce the no-slip condition at the interface. The method is validated through comparisons with exact solutions for oneand two-dimensional problems. The method is then used to simulate the solidification processes with the effects of volume change due to density difference.

Direct numerical simulation of solidification with effects of density difference