Smoothed particle hydrodynamics for free-surface and multiphase flows: a review

The smoothed particle hydrodynamics (SPH) method is expanding and is being applied to more and more fields, particularly in engineering. The majority of current SPH developments deal with free-surface and multiphase flows, especially for situations where geometrically complex interface configurations are involved. The present review article covers the last 25 years of development of the method to simulate such flows, discussing the related specific features of the method. A path is drawn to link the milestone articles on the topic, and the main related theoretical and numerical issues are investigated. In particular, several SPH schemes have been derived over the years, based on different assumptions. The main ones are presented and discussed in this review underlining the different contexts and the ways in which they were derived, resulting in similarities and differences. In addition, a summary is provided of the recent corrections proposed to increase the accuracy, stability and robustness of SPH schemes in the context of free-surface and multiphase flows. Future perspectives of development are identified, placing the method within the panorama of Computational Fluid Dynamics.