Stabilizing S.P.H. with conservative smoothing

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Abstract
There is an instability in certain S.P.H. (Smoothed Particle Hydrodynamics method) material dynamics computations. Evidence from analyses and experiments suggests that the instabilities in S.P.H. are not removable with artificial viscosities. However, the analysis shows that a type of conservative smoothing does remove the instability. Also, numerical experiments, on certain test problems, show that SPHCS, and S.P.H. code with conservative smoothing, compares well in accuracy with computations based on the von Neumann-Richtmyer method.

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