An Accurate SPH Scheme for Dynamic Fragmentation modelling

We focus on the use of a meshless numerical method called Smooth Particle Hydrodynamics (SPH), to solve fragmentation issues as Hyper Velocity Impact (HVI) cases. Firstly applied to fluid flow simulations, this method can be extended to the solid dynamics framework. However it suffers from a lack of accuracy when evaluating state variables as the pressure field. And such inaccuracy generally generates non-physical processes (as numerical fragmentation). In the hydrodynamic context, SPH-ALE methods based on Riemann solvers significantly improve this evaluation, but increase the scheme complexity and low-Mach issues are difficult to prevent. We propose an alternative scheme called γ-SPH-ALE, firstly implemented to solve multi-regime barotropic flows, and secondly extended to solid dynamic cases. It relies on the combination of the SPH-ALE formalism and a finite volume stabilizing low-Mach scheme. Its characteristics are detailed and evaluated through a nonlinear stability analysis, highlighting CFL-like conditions on the scheme parameters. Finally, its implementation on several test cases reveals that the proposed scheme actually increases both stability and accuracy, in reduced computation time, with respect to classical solvers