Adaptive tetrahedral meshing in free-surface flow

An unstructured, three-dimensional, moving-mesh algorithm is developed for free-surface flows with the capability of simulating large deformation. A robust edge swapping algorithm and an optimization-based mesh smoothing algorithm are used to improve mesh quality as the interface deforms. The edge swapping algorithm uses an optimal swap sequence to transform configurations with several tetrahedra sharing a common edge. The optimization-based mesh smoothing relocates vertex position so that the minimum quality of the incident cells is maximized. Also, edge contraction and bisection are used to adjust the mesh resolution according to surface curvature. These local refinements effectively maintain good mesh quality and appropriate mesh size while avoiding global re-meshing. This scheme's robustness and accuracy are demonstrated with deforming liquid ligaments, periodic jets, and colliding droplets.