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Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. (English) Zbl 0962.76075
Summary: We present a new variational framework for various existing smooth particle hydrodynamic (SPH) techniques, and give a new corrected SPH formulation. The linear and angular momentum preserving properties of SPH formulations are also discussed. We show that, in general, in order to preserve angular momentum, the SPH equations must correctly evaluate the gradient of linear velocity field, and hence we propose a corrected algorithm that combines kernel correction with gradient correction. The theory presented is illustrated with several examples related to simple free surface flows.

76M28 Particle methods and lattice-gas methods
76M30 Variational methods applied to problems in fluid mechanics
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