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arXiv · 2504.04048

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

Shijun Liao·Shijie Qin
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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, respectively. 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.

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Shijun Liao, Shijie Qin. 2025-04-05. Physical significance of artificial numerical noise in direct numerical simulation of turbulence. https://doi.org/10.1017/jfm.2025.200

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