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Moving least-squares particle hydrodynamics. II: Conservation and boundaries. (English) Zbl 0960.76068
Summary: In part I the author [ibid. 44, No. 8, 1115-1155 (1999; Zbl 0951.76074)] has shown that the consistency of the smooth particle hydrodynamics (SPH) method can be improved to acceptable levels by substituting moving least squares (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. Here we describe a new locally conservative MLS variant of SPH that naturally incorporates realistic boundary conditions. In order to provide for the boundary fluxes, one must identify the boundary particles. Thus we present a new, purely geometric boundary detection technique for assemblies of spherical particles. A comparison with SPH on a ball-and-plate impact simulation shows qualitative improvement.

76M28Particle methods and lattice-gas methods (fluid mechanics)
74M20Impact (solid mechanics)
74J40Shocks and related discontinuities (waves in solid mechanics)
76L05Shock waves; blast waves (fluid mechanics)