| An unstructured, three-dimensional, moving-mesh algorithm is developed for free-surface flow simulations with large deformations. This method moves the surface mesh to follow the free surface in a Lagrangian manner, therefore it can exactly track the evolving surface.; In order to simulate large deformation and maintain good mesh quality at the same time, robust mesh reconnection and smoothing algorithms are implemented. The mesh reconnection algorithm performs local topological changes to improve the quality of a structure of several tetrahedra sharing a common edge. A dynamic programming technique is used to search for the best reconnection scheme for such a structure. Optimization-based mesh smoothing is used to move the interior nodes, in which a free vertex is moved so that the minimum quality of the tetrahedra attached to this vertex is maximized.; To capture the varied length scales of the evolving free surface, a mesh adaptation scheme using edge contraction and bisection is implemented. This scheme effectively adds and removes elements to accommodate to the local length scales. To improve computational efficiency, a lower bound is imposed on the edge lengths, and a surface fairing (diffusion) scheme is used to remove the disturbances caused by the under-resolution of surface curvature due to this lower bound.; The effects of these techniques are demonstrated with simulations of deforming liquid ligaments, periodic jets, and colliding droplets. The results are in good agreement with analytical solutions and experimental data. |
