The breakdown of Navier—Stokes hydrodynamics in small periodic systems

Abstract

The results of direct particle simulations of 2-dimensional, convective flow are compared with truncated solutions of the Navier—Stokes equation, and show that the Navier—Stokes predictions are quite accurate throughout the transient development of the flow, if the correct value of the viscosity is used. The viscosity determines the steady values of the flow velocities, and the Navier—Stokes predictions are accurate for systems with multiple k vector forcing. At higher values of the fields, there is a limiting value of the forcing for which the character of the response matches the character of the forcing. Beyond this point there is a breakdown in hydrodynamic behaviour where the particle nature of the fluid dominates. Both multiphase solid and fluid regions are observed, plus cavitation, depending upon the forcing and the system geometry.