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High-order moment closure models with random batch method for efficient computation of multiscale turbulent systems.

Di Qi1, Jian-Guo Liu2

  • 1Department of Mathematics, Purdue University, 150 North University Street, West Lafayette, Indiana 47907, USA.

Chaos (Woodbury, N.Y.)
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Summary

We developed a high-order stochastic-statistical moment closure model using the random batch method (RBM) for efficient turbulent system prediction. This method accurately captures complex statistics and extreme events with reduced computational cost.

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Area of Science:

  • * Computational fluid dynamics
  • * Applied mathematics
  • * Statistical modeling

Background:

  • * Multiscale complex turbulent systems present challenges in accurate statistical moment and probability density function prediction.
  • * Traditional ensemble simulations are computationally expensive, especially for high-dimensional systems with closely coupled spatiotemporal scales.
  • * Modeling non-Gaussian statistics and extreme events requires advanced closure models.

Purpose of the Study:

  • * To propose a high-order stochastic-statistical moment closure model for efficient ensemble prediction.
  • * To introduce computational strategies, specifically the random batch method (RBM), to reduce ensemble size and computational cost.
  • * To develop a reduced-order model for high-dimensional systems by linking small-scale fluctuations to dominant modes.

Main Methods:

  • * Development of a high-order stochastic-statistical moment closure model.
  • * Implementation of the random batch method (RBM) for efficient ensemble simulations.
  • * Creation of a reduced-order model linking small-scale fluctuation modes to dominant ensemble modes.
  • * Validation using one-layer and two-layer Lorenz '96 systems.

Main Results:

  • * The RBM models accurately capture leading-order statistics and non-Gaussian probability distributions.
  • * Significant reduction in computational cost compared to direct Monte Carlo methods.
  • * Both full and reduced-order RBM models demonstrate high predictive skill.
  • * Effective handling of chaotic features and diverse statistical regimes.

Conclusions:

  • * The proposed high-order stochastic-statistical moment closure model with RBM offers an efficient approach for turbulent system prediction.
  • * The models successfully capture complex statistical phenomena, including extreme events.
  • * These models provide valuable tools for prediction, uncertainty quantification, and data assimilation in various applications.