Mass Matrix Formulation of the FLIP Particle-in-Cell Method

A refinement of FLIP [ Brackbill and Ruppel, J. Comput. Phys.65, 314 (1986) ] is described which uses a mass matrix formulation to achieve greater accuracy and less numerical diffusion over the previous version. Without the refinement, there is a significant dissipation of energy in modeling elastic vibrations of a solid. Moreover, in modeling an initial flow discontinuity there are sub-grid-scale oscillations in the particle velocity field in the neighborhood of the discontinuity. These difficulties are eliminated using the mass matrix. In addition, the mass matrix formulation conserves kinetic energy, linear and angular momentum, and is Galilean invariant.