Abstract
This study shows formulation of ISPH (Incompressible Smoothed Particle Method ) using Lagrange's equation of the first kind. The formulation by Lagrange's equation of the first kind determine the equation expressions of pressure gradient and velocity divergence uniquely. Moreover, adding constraint condition of fluid particles and wall particles into the Lagrangian causes repulsive force of fluid particle from wall boundary. While penetration of fluid particles into wall boundary often happens in the conventional IPSH formulation, the penetration can be prevented by applying the new formulation. Two numerical problems, simple one-dimensional problem and three-dimensional dam break problem, are solved to show the validity of the proposed method.
