Delaunay triangulation and free surface extraction for SPH method

Smoothed particle hydrodynamics (SPH) is a meshfree, Lagrangian particle method, which combines the best features of Eulerian and Lagrangian grid-based methods, and has been successfully applied to different areas in sciences and engineering. The post-processing of SPH is not as straight forward and convenient as the grid-based methods since the information is based on irregularly distributed particles rather than on a grid system. Moreover, free surfaces are usually difficult to be reconstructed or extracted based simply on SPH particles. In this paper, a Delaunay triangulation is developed, in which a triangular mesh is generated form SPH particles through Delaunay triangulation, and the related information on SPH particles is converted to the triangular mesh. The SPH post-processing can then be conducted on the triangular mesh rather than on the SPH particles. Also free surfaces can be extracted from the generated Delaunay mesh. Two typical examples, the head-on collision of two liquid drops and dam collapse have been simulated. The obtained results with precisely extracted free surfaces demonstrate the effectiveness of the approach of Delaunay triangulation and free surface extraction for SPH method.