Hamiltonian moving-particle semi-implicit (HMPS) method for incompressible fluid flows

Particle methods are meshless simulation techniques in which motion of continua is approximated by discrete dynamics of a finite number of particles, and thus have a great degree of flexibility, for instance, in dealing with the complex motion of surfaces or boundaries. In this paper, a particle method is developed from a direct discretization of the Lagrangian for inviscid incompressible fluid flows. The discretized Lagrangian is transformed into a Hamiltonian with holonomic constraints that stem from the incompressibility condition. The RATTLE algorithm that is a symplectic scheme for holonomically constrained Hamiltonian systems is adopted so that the resulting particle method inherits structures possessed by the partial differential equations that govern inviscid incompressible flows. The algorithm of the particle method is semi-implicit, so we call it the Hamiltonian moving-particle semi-implicit (HMPS) method. Some numerical tests indicate the excellence of the HMPS method in conservation of mechanical energy (as well as linear and angular momenta).