Physics-Constrained Neural Closure for Lattice Boltzmann Large-Eddy Simulation

TL;DR

This paper introduces a physics-constrained neural network for subgrid-scale stress modeling in lattice Boltzmann large-eddy simulations, improving accuracy and efficiency over traditional methods.

Contribution

It develops a novel neural closure model trained on DNS data, incorporating physics constraints and compatible with LBM, enhancing LES accuracy.

Findings

Good agreement with DNS stress data

Improved energetic statistics over Smagorinsky models

Efficient deployment with ONNX Runtime

Abstract

We present a physics-constrained, data-driven subgrid-scale (SGS) stress closure for large-eddy simulation (LES) in the lattice Boltzmann method (LBM). Trained on filtered-downsampled (FD) data from LBM direct numerical simulation (DNS) of forced homogeneous isotropic turbulence (FHIT) spanning multiple filter widths, a compact neural network maps nine macroscopic derivative inputs - six strain-rate and three vorticity components - to the six independent components of the SGS stress tensor; a deviatoric projection is applied post-inference to obtain the traceless stress used in the solver. Training combines a stress data loss with physics terms for SGS energy-transfer (Pi) matching, rotational equivariance under cube rotations, and compatibility of the implied SGS forcing with the divergence-based coupling. The predicted stress is coupled to the solver through a split strategy: a dissipative, strain-aligned contribution is represented through an effective-viscosity projection, while the remaining anisotropic residual is applied through a forcing term. This construction is intended to retain both backscatter (via the effective viscosity) and non-dissipative anisotropic effects (via the residual forcing), while remaining compatible with LBM deployment. In the cases considered here, a priori results show good agreement with FD references across stress components and SGS-transfer statistics, and a posteriori rollouts improve several energetic and statistical measures relative to static and dynamic Smagorinsky baselines. A preliminary transfer test in turbulent channel flow is also reported without retraining. Finally, we demonstrate production deployment via ONNX Runtime, with throughput comparable to a dynamic Smagorinsky baseline in the tested configuration.