Direct statistical simulation of the Lorenz96 system in model reduction approaches

Journal Article · 26 January 2025 · Physical Review. E

DOI: https://doi.org/10.1103/PhysRevE.111.015308 · OSTI ID:2507124

Li, Kuan; Tobias, Steven M.; Marston, J. B.

Direct statistical simulation (DSS) of nonlinear dynamical systems bypasses the traditional route of accumulating statistics by lengthy direct numerical simulations by solving the equations that govern the statistics themselves. DSS suffers, however, from the curse of dimensionality as the statistics (such as correlations) generally have higher dimensions than the underlying dynamical variables. Here we investigate two approaches to reduce the dimensionality of DSS, illustrating each method with numerical experiments with the Lorenz96 dynamical system. The forms of DSS chosen here involve approximate closures at second and third order in the equal-time cumulants. We demonstrate significant reduction in computational effort that can be achieved without sacrificing the accuracy of DSS. The methods developed here can be applied to turbulent fluid and magnetohydrodynamical systems. Published by the American Physical Society 2025

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0024572
• OSTI ID: 2507124
• Journal Information: Physical Review. E, Journal Name: Physical Review. E Journal Issue: 1 Vol. 111; ISSN PLEEE8; ISSN 2470-0045
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English