A physically consistent particle method for incompressible fluid flow calculation

In general, mechanical energy monotonically decreases in a physically consistent system, constructed with conservative force and dissipative force. This feature is important in designing a particle method, which is a discrete system approximating continuum fluid with particles. When the discretized system can be fit into a framework of analytical mechanics, it will be a physically consistent system which prevents instability like particle scattering along with unphysical mechanical energy increase. This is the case also in incompressible particle methods. However, most incompressible particle methods do not satisfy the physical consistency, and they need empirical relaxations to suppress the system instability due to the unphysical energy behavior. In this study, a new incompressible particle method with the physical consistency, moving particle full-implicit (MPFI) method, is developed, where the discretized interaction forces are related to an analytical mechanical framework for the systems with dissipation. Moreover, a new pressure evaluation technique based on the virial theorem is proposed for the system. Using the MPFI method, static pressure, droplet extension, standing wave and dam break calculations were conducted. The capability to predict pressure and motion of incompressible free surface flow was presented, and energy dissipation property depending on the particle size and time step width was studied through the calculations.