Moving least-squares particle hydrodynamics II: conservation and boundaries

Previous work by the author has shown that the consistency of the SPH method can be improved to acceptable levels by substituting MLS interpolants for SPH interpolants, that the SPH inconsistency drives the tension instability and that imposition of consistency via MLS severely retards tension instability growth. The new method however was not conservative, and made no provision for boundary conditions. Conservation is an essential property in simulations where large localized mass, momentum or energy transfer occurs such as high-velocity impact or explosion modeling. A new locally conservative MLS variant of SPH that naturally incorporates realistic boundary conditions is described. In order to provide for the boundary #uxes one must identify the boundary particles. A new, purely geometric boundary detection technique for assemblies of spherical particles is described. A comparison with SPH on a ball-and-plate impact simulation shows qualitative improvement.