Variational and momentum preservation aspects of Smooth Particle Hydrodynamic formulations

This paper presents a new variational framework for various existing: Smoot h Particle Hydrodynamic (SPH) techniques and presents a new corrected SPH f ormulation. The linear and angular momentum preserving properties of SPH fo rmulations are also discussed. The paper will show that in general in order to preserve angular momentum, the SPH equations must correctly evaluate th e gradient of a linear velocity field. A corrected algorithm that combines kernel correction with gradient correction is presented. The paper win illu strate the theory presented with several examples relating to simple free s urface flows. (C) 1999 Elsevier Science S.A. All rights reserved.