Verifiability and Limit Consistency of Eddy Viscosity Large Eddy Simulation Reduced Order Models
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908378375127040 |
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| author | Reyes, Jorge Tsai, Ping-Hsuan Moore, Ian Liu, Honghu Iliescu, Traian |
| author_facet | Reyes, Jorge Tsai, Ping-Hsuan Moore, Ian Liu, Honghu Iliescu, Traian |
| contents | 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 \emph{``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: (i) the 1D Burgers equation with a small diffusion coefficient; and (ii) the 2D lid-driven cavity flow at Reynolds number $Re=15,000$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18310 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Verifiability and Limit Consistency of Eddy Viscosity Large Eddy Simulation Reduced Order Models Reyes, Jorge Tsai, Ping-Hsuan Moore, Ian Liu, Honghu Iliescu, Traian Fluid Dynamics Numerical Analysis 65M15, 65M60, 76D05, 76F65 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 \emph{``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: (i) the 1D Burgers equation with a small diffusion coefficient; and (ii) the 2D lid-driven cavity flow at Reynolds number $Re=15,000$. |
| title | Verifiability and Limit Consistency of Eddy Viscosity Large Eddy Simulation Reduced Order Models |
| topic | Fluid Dynamics Numerical Analysis 65M15, 65M60, 76D05, 76F65 |
| url | https://arxiv.org/abs/2505.18310 |