A random batch method for efficient ensemble forecasts of multiscale turbulent systems.

Area of Science:

• Fluid Dynamics
• Computational Science
• Statistical Modeling

Background:

• Multiscale turbulent systems involve complex interactions between large and small-scale variables.
• High-dimensional simulations of these systems incur significant computational expense.
• Existing ensemble prediction strategies struggle with the computational cost of large simulations.

Purpose of the Study:

• To develop an efficient ensemble prediction strategy for multiscale turbulent models.
• To reduce the computational burden associated with large ensemble simulations.
• To improve the accuracy and applicability of turbulent flow predictions.

Main Methods:

• A random batch decomposition strategy is employed to manage the wide spectrum of fluctuation states.
• Ensemble samples are updated using small portions of small-scale fluctuation modes per batch.
• Frequent random resampling ensures the multiscale coupling and true model dynamics are maintained.
• Theoretical convergence of statistical errors and numerical forecast skill were investigated.

Main Results:

• The random batch method's statistical error convergence is independent of sample size and system dimension.
• The method accurately captures key statistical phenomena in turbulent flows, including non-Gaussian distributions and intermittent bursts.
• Forecast skill was validated on two representative turbulent flow models.
• Computational cost is significantly lower compared to direct ensemble approaches.

Conclusions:

• The proposed random batch method offers an efficient and accurate approach for multiscale turbulent model prediction.
• This strategy effectively handles complex statistical features of turbulent flows.
• The method provides a foundation for enhanced uncertainty quantification and data assimilation in complex systems.