Is a direct numerical simulation (DNS) of Navier-Stokes equations with small enough grid spacing and time-step definitely reliable/correct?

Qin, Shijie; Yang, Yu; Huang, Yongxiang; Mei, Xinyu; Wang, Lipo; Liao, Shijun

doi:10.1016/j.joes.2024.04.002

Journal of Ocean Engineering and Science

2024

DOI: 10.1016/j.joes.2024.04.002

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Is a direct numerical simulation (DNS) of Navier-Stokes equations with small enough grid spacing and time-step definitely reliable/correct?

Shijie Qin,

Yu Yang,

Yongxiang Huang

et al.

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2024

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Cited by 3 publications

References 63 publications

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Influences of artificial numerical noise on statistics and qualitative properties of chaotic system

Qin,

Liao

2024

Physica D: Nonlinear Phenomena

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Influences of artificial numerical noise on statistics and qualitative properties of chaotic system

Qin,

Liao

2024

Physica D: Nonlinear Phenomena

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Cascades and Kolmogorov's lognormal scaling in two-dimensional bacterial turbulence

Huang

2024

Physics of Fluids

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Collective movements of bacteria exhibit a remarkable pattern of turbulence-like vortices, in which the Richardson cascade plays an important role. In this work, we examine the energy and enstrophy cascades and their associated lognormal statistics using experimental velocity field data. The coherent structure observed on a large scale is due to the presence of the inverse energy cascade, while the kinetic energy is dissipated at all scales, since these active movements occur below the fluid viscosity scale. The forward enstrophy cascade occurs with injection at all scales and may be represented by other nonlinear interactions that are not captured by the existing experimental data. Furthermore, the lognormal statistics for both energy dissipation and enstrophy fields is verified in accordance with the Kolmogorov 1962 refined theory of turbulence. Their scaling exponents can be well described by the lognormal formula with intermittency parameters comparable with those of the three-dimensional hydrodynamic turbulence. The joint analysis of the multifractal measures of the energy dissipation rate and enstrophy follows an ellipse model from the lognormal statistics. Our results confirm the coexistence of the inverse energy cascade and the intermittency correction of the velocity scaling in this active fluid system. An inverse energy cascade diagram below the fluid viscosity is summarized to describe the observed two-dimensional bacterial turbulence. Our work provides an example of an active-flow model benchmark.

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Ultra-Chaos: A Great Challenge for Machine Learning and AI

Yang,

Liao

2024

Int. J. Bifurcation Chaos

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Machine Learning (ML) is highly data dependent. But all data contain noise. Especially for chaotic systems, due to the famous “butterfly-effect”, small disturbances can grow exponentially to the same order of magnitude as the physical solution so that numerical simulations of chaos become badly polluted. A fundamental and open problem is how data noise in chaotic systems influences short and long-term predictions of ML based on such badly polluted data. Ultra-chaos, whose statistics are sensitive to small disturbances, is a new concept in chaos theory. In this paper, the influence of data noise on ML of chaos is investigated in detail by comparing predictions with three ML models based on a “clean” dataset given by Clean Numerical Simulation (CNS), and a “badly polluted” dataset given by the traditional Runge–Kutta method. It is found that neither data noise nor ML prediction deviation influence the long-term statistics of ML predictions for normal-chaos. However, data noise has a significant influence on the statistics of ML predictions for ultra-chaos: this might pose a great challenge for ML that is a part of AI.

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Is a direct numerical simulation (DNS) of Navier-Stokes equations with small enough grid spacing and time-step definitely reliable/correct?

Cited by 3 publications

References 63 publications

Influences of artificial numerical noise on statistics and qualitative properties of chaotic system

Influences of artificial numerical noise on statistics and qualitative properties of chaotic system

Cascades and Kolmogorov's lognormal scaling in two-dimensional bacterial turbulence

Ultra-Chaos: A Great Challenge for Machine Learning and AI

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