Globally time-reversible fluid simulations with smoothed particle hydrodynamics

This paper describes an energy-preserving and globally time-reversible code for weakly compressible smoothed particle hydrodynamics (SPH). We do not add any additional dynamics to the Monaghan's original SPH scheme at level of ordinary differential equation, but we show how discretize equations by using a corrected expression density invoking symplectic integrator. Moreover, achieve global-in-time reversibility, have correct initial state, implement conservative fluid-wall interaction, use fixed-point arithmetic. Although numerical is reversible in time (solvable backwards while recovering conditions), observe thermalization velocities growth Boltzmann entropy. In other words, when see all possible details, as entropy, which depends only on one-particle distribution function, emergence second law thermodynamics (irreversible behavior) from purely dynamics.