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Published on: December 4, 2017
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High-order moment closure models with random batch method for efficient computation of multiscale turbulent systems.
1Department of Mathematics, Purdue University, 150 North University Street, West Lafayette, Indiana 47907, USA.
Chaos (Woodbury, N.Y.)
|October 23, 2023
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.
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.
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