Data Assimilation in Large Eddy Simulation: Addressing Model-Observation Mismatch from Navier-Stokes Data

2025/08/10 by Adam Larios, Larios, Adam, Ali Pakzad +3
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #35B40 #35K55 #35Q30 #76D05 #76F65 #93E11 #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Meteorological Phenomena and Simulations #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2508.07492

openalex publication_date 2025/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In atmospheric and turbulent flow modeling, Large Eddy Simulation (LES) is often used to reduce computational cost, while observational data typically originates from the underlying physical system. Motivated by this setting, we study a continuous data assimilation (CDA) algorithm applied to a Smagorinsky/Ladyzhenskaya-type LES model, in which the observational data is generated from the full Navier--Stokes equations (NSE). In the two-dimensional setting, we establish global well-posedness of the assimilated system and prove exponential convergence to the true solution, up to an error of order ν^1/2, where ν is the turbulence viscosity parameter. In addition to rigorous analysis in 2D, we provide numerical simulations in both 2D domains with physical boundary conditions and 3D periodic domains, demonstrating effective synchronization in these cases, and corroborating our theoretical predictions.

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Related

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• Sparse data assimilation for under-resolved large-eddy simulations