Variational time integrators

In this paper, we propose a Galerkin-based smoothed particle hydrodynamics (SPH) formulation with moving least-squares meshless approximation, applied to free surface flows. The Galerkin scheme provides a clear framework to analyse several procedures widely used in the classical SPH literature, suggesting that some of them should be reformulated in order to develop consistent algorithms. The performance of the methodology proposed is tested through various dynamic simulations, demonstrating the attractive ability of particle methods to handle severe distortions and complex phenomena