The role of time integration in energy conservation in Smoothed Particle Hydrodynamics fluid dynamics simulations

The choice of a time integration scheme is crucial aspect any transient fluid simulation, and Smoothed-Particle Hydrodynamics (SPH) no exception. influence the on energy balance here addressed. To do so, explicit expressions allowing to compute deviations from balance, induced by scheme, are provided. These expressions, computed \textit{a posteriori}, valid for different methods. Such formulation tested with simulation two-dimensional non-viscous impact two jets, artificial dissipation terms. best our knowledge, this first stable non-dissipative system weakly-compressible SPH method. A viscous case, Taylor-Green vortex, has also been simulated. Results show that an implicit behaves better in context.