Smoothed particle hydrodynamics (sph)
Smoothed Particle Hydrodynamics (SPH) is a Lagrangian Particle method, where the discretization points are advected in time with the flow field. First introduced independently of Lucy  and Gingold and Monaghan  in 1977, SPH was originally used to simulate three-dimensional astrophysics problems. This Lagrangian framework enabled the simulation of star formations and interactions of different galaxies where grid-based methods failed mainly due to the problem of large computational domains. Over the years, SPH was applied to a lot of different problems ranging from structural analysis  to free-surface flows  or even microscopic multi-phase flows . SPH is our method of choice, because it is advantageous especially for multi-phase problems with moving and deforming interfaces. The more, contrary to grid-based methods mass conservation on the interface can be achieved exactly and no interface capturing scheme is needed.
- L. Lucy, A numerical approach to the testing of the fission hypothesis, Astron. J. 82 (1977), 1013.
- R.A. Gingold, J.J. Monaghan, Smoothed particle hydrodynamics: Theory and application to non-spherical stars, Mon. Not. R. Astron. Soc 181 (1977), 375.
- C. Antoci, M. Gallati, S. Sibilla, Numerical simulation of fluid-structure interaction by SPH, Comput. & Structures 85(11-14) (2007) 879-890.
- J.J. Monaghan, Simulating free surface flows with SPH, J. Comput. Phys. 110 (1994) 399-399.
- X.Y. Hu, N.A. Adams, A multi-phase SPH method for macroscopic and mesoscopic flows, J. Comput. Phys. 213(2) (2006) 844-861.