Time-reversible continuum mechanics

Abstract

Levesque and Verlet developed a time-reversible and “bit-reversible” computational leapfrog algorithm. Their algorithm uses integer arithmetic and is exactly time reversible to the last computational bit describing the particle coordinates. We generalize their idea, developed for atomistic molecular dynamics, to smoothed-particle continuum mechanics. In the special case of a two-dimensional isentropic ideal gas, these two approaches, one microscopic and the other macroscopic, are isomorphic. In the more general nonadiabatic case, but still without dissipative terms, our continuum extension of the leapfrog scheme remains stable and also exhibits the exact time and bit reversibility associated with Levesque and Verlet's atomistic approach.