Physical significance of artificial numerical noise in direct numerical simulation of turbulence

Abstract

Using clean numerical simulation (CNS) in which artificial numerical noise is negligible over a finite, sufficiently long interval of time, we provide evidence, for the first time, that artificial numerical noise in direct numerical simulation (DNS) of turbulence is approximately equivalent to thermal fluctuation and/or stochastic environmental noise. This confers physical significance on the artificial numerical noise of DNS of the Navier-Stokes equations. As a result, DNS on a fine mesh should correspond to turbulence under small internal/external physical disturbance, whereas DNS on a sparse mesh corresponds to turbulent flow under large physical disturbance. The key point is that all of them have physical meanings and so are correct in terms of their deterministic physics, even if their statistics are quite different. This is illustrated herein. Our paper provides a positive viewpoint regarding the presence of artificial numerical noise in DNS.