Abstract
The stabilized ISPH method is a kind of particle methods for the incompressible Navier-Stokes equations and is defined as an incompressible SPH method with a pressure Poisson equation added with a stabilization term with respect to density of particles. By some numerical experiments in previous studies, it has been verified that the stabilization term contributes to avoiding a localization of particles; then, numerical results with a computational stability, volume conservation, and higher accuracy have been obtained. However, because the stabilization term is derived from a discretization of the continuity equation of compressible fluid, it is not clarified whether the stabilization term contributes to keeping uniformness of particle distributions theoretically. Therefore, based on mathematical theory alone, the stabilization term is derived as an approximate solution of an energy minimization problem with respect to errors of incompressibility of fluid and uniformness of particle distributions.
