A CURVILINEAR LEVEL SET FORMULATION FOR HIGHLY DEFORMABLE FREE SURFACE PROBLEMS WITH APPLICATION TO SOLIDIFICATION

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Abstract
A curvilinear level set formulation has been developed for highly deformable free surface problems. In this new scheme, the grid lines follow the irregular domain generated by the multizone adaptive grid-generation (MAGG) scheme [1] and free surfaces are captured by level set functions among the curvilinear grids. Navier-Stokes equations are discretized and solved based on a multiphase curvilinear finite-volume method [2], and the level set function is solved based on a finite-difference method using the second-order essentially nonoscillatory (ENO) scheme [3]. The scheme is capable of accurately and efficiently representing the deformation, oscillation, merger, and separation of free surfaces. The effectiveness and robustness of the algorithm are demonstrated by using it for problems involving merger of bubbles, mold filling, and the spreading and solidification of molten droplets on a cold substrate where both free surface and solidification interfaces move and the mass of the liquid phase is continuously decreased.