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

Abstract

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

arXiv comment46 pages, 15 figures

References in corpus (4)

• Improving convergence in smoothed particle hydrodynamics simulations without pairing instability
• Modelling discontinuities and Kelvin-Helmholtz instabilities in SPH
• Investigation of wall bounded flows using SPH and the unified semi-analytical wall boundary conditions
• A geometric formulation of the Shepard renormalization factor

Cited by in corpus (3)

• A unified derivation of Voronoi, power, and finite-element Lagrangian computational fluid dynamics
• Boundary conditions for SPH through energy conservation
• Shock-capturing particle hydrodynamics with reproducing kernels