Work

Verifiability and Limit Consistency of Eddy Viscosity Large Eddy Simulation Reduced Order Models

Year: 2025

Type: article

Abstract: Large eddy simulation reduced order models (LES-ROMs) are ROMs that leverage LES ideas (e.g., filtering and closure modeling) to construct accurate and efficient ROMs for convection-dominated (e.g., turbulent) flows. Eddy viscosity (EV) ROMs (e.g., Smagorinsky ROM (S-ROM)) are LES-ROMs whose closure model consists of a diffusion-like operator in which the viscosity depends on the ROM velocity. We propose the Ladyzhenskaya ROM (L-ROM), which is a generalization of the S-ROM. Furthermore, we prove two fundamental numerical analysis results for the new L-ROM and the classical S-ROM: (i) We prove the verifiability of the L-ROM and S-ROM, i.e., that the ROM error is bounded (up to a constant) by the ROM closure error. (ii) We introduce the concept of ROM limit consistency (in a discrete sense), and prove that the L-ROM and S-ROM are limit consistent, i.e., that as the ROM dimension approaches the rank of the snapshot matrix, d , and the ROM lengthscale goes to zero, the ROM solution converges to the “true solution" , i.e., the solution of the d -dimensional ROM. Finally, we illustrate numerically the verifiability and limit consistency of the new L-ROM and S-ROM in two under-resolved convection-dominated problems that display sharp gradients: the 1D Burgers equation with a small diffusion coefficient; and the 2D lid-driven cavity flow at Reynolds number $$\textrm{Re}=15,000$$ Re = 15 , 000 .

Source: Journal of Scientific Computing

DOI: 10.1007/s10915-025-03106-6

Authors: Jorge Reyes, Ping-Hsuan Tsai, Ian Moore, Honghu Liu, Traian Iliescu

Institution: Virginia Tech

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: National Science Foundation, Directorate for Mathematical and Physical Sciences