Globally time-reversible fluid simulations with smoothed particle hydrodynamics

TL;DR

This paper presents a novel energy-preserving, globally time-reversible smoothed particle hydrodynamics code that demonstrates how reversible microscopic dynamics can lead to macroscopic irreversibility and entropy growth.

Contribution

It introduces a symplectic integrator and correction techniques to achieve global time-reversibility in SPH simulations, revealing thermodynamic behavior from reversible equations.

Findings

The scheme is reversible in principle but shows entropy growth in practice.

Reversible dynamics can produce irreversible thermodynamic phenomena.

The method preserves energy and reversibility over long simulations.

Abstract

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