Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Physics-informed data-driven inference of an interpretable equivariant LES model of incompressible fluid turbulence

Matteo Ugliotti, Brandon Choi, Mateo Reynoso, Daniel R. Gurevich, Roman O. Grigoriev

Abstract

Restrictive phenomenological assumptions represent a major roadblock for the development of accurate subgrid-scale models of fluid turbulence. Specifically, these assumptions limit a model's ability to describe key quantities of interest, such as local fluxes of energy and enstrophy, in the presence of diverse coherent structures. This paper introduces a symbolic data-driven subgrid-scale model that requires no phenomenological assumptions and has no adjustable parameters, yet it outperforms leading LES models. A combination of a priori and a posteriori benchmarks shows that the model produces accurate predictions of various quantities including local fluxes across a broad range of two-dimensional turbulent flows. While the model is inferred using LES-style spatial coarse-graining, its structure is more similar to RANS models, as it employs an additional field to describe subgrid scales. We find that this field must have a rank-two tensor structure in order to correctly represent both the components of the subgrid-scale stress tensor and the various fluxes.

Physics-informed data-driven inference of an interpretable equivariant LES model of incompressible fluid turbulence

Abstract

Restrictive phenomenological assumptions represent a major roadblock for the development of accurate subgrid-scale models of fluid turbulence. Specifically, these assumptions limit a model's ability to describe key quantities of interest, such as local fluxes of energy and enstrophy, in the presence of diverse coherent structures. This paper introduces a symbolic data-driven subgrid-scale model that requires no phenomenological assumptions and has no adjustable parameters, yet it outperforms leading LES models. A combination of a priori and a posteriori benchmarks shows that the model produces accurate predictions of various quantities including local fluxes across a broad range of two-dimensional turbulent flows. While the model is inferred using LES-style spatial coarse-graining, its structure is more similar to RANS models, as it employs an additional field to describe subgrid scales. We find that this field must have a rank-two tensor structure in order to correctly represent both the components of the subgrid-scale stress tensor and the various fluxes.
Paper Structure (19 sections, 37 equations, 19 figures)

This paper contains 19 sections, 37 equations, 19 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Governing Equations and Coarse-Graining
  4. SGS Stress Tensor Decomposition and Moment Expansion
  5. Physically-informed data-driven equation inference
  6. Results
  7. Model inference
  8. A priori Benchmarks
  9. Stability and Regularization
  10. A posteriori Benchmarks
  11. Freely Decaying Turbulence
  12. Forced Turbulence
  13. Discussion
  14. Conclusion
  15. Computational Details & DNS
  16. ...and 4 more sections

Figures (19)

  • Figure 1: Initial conditions for the three flows F1 (a), F2 (b), and F3 (c). The characteristic integral scale is, respectively, $\ell_i \approx \ell_d/30$, $\ell_d/4$, and $\ell_d/2$.
  • Figure 2: A priori benchmarks for the flows F1 (a), F2 (b), and F3 (c) with $\nu = 10^{-5}$: the accuracy of the SGS stress tensor $\mathcal{A}(\tau)$, local energy flux $\mathcal{A}(\Pi)$, and mean energy flux normalized by the DNS value $\langle\Pi^{\rm LES}\rangle/\langle\Pi^{\rm NDS}\rangle$. Five LES models are compared: NGMR (blue), NGM4 (orange), similarity (yellow), unclipped dynamic mixed (purple), and unclipped dynamic Smagorinsky (green), each averaged in time over the dataset.
  • Figure 3: A priori energy flux for $\delta = 0.3$ for the state shown in panel (a). The black box delineates the region shown in the remaining panels. Panel (b) shows the details of the vorticity field. The remaining panel show the flux corresponding to (c) FDNS, (d) NGMR, (e) NGM4, (f) similarity model, (g) dynamic Smagorinsky, and (h) dynamic mixed model. The flux is shown without backscatter clipping.
  • Figure 4: Correlation for the $R$ evolution equation. The datasets correspond to the flows F3 (blue), F2 (orange), and F1 (yellow).
  • Figure 5: Snapshots of numerical solutions of NGMR for freely decaying turbulence at $\nu = 10^{-7}$ on a $256\times256$ grid. The vorticity field computed with (a-c) and without (d-f) the regularizing terms \ref{['reg_1']} and \ref{['reg_2']} is shown at $t=0$ (a,d), $t=20T_e$ (b,e), and $t=60T_e$ (c,f).
  • ...and 14 more figures