Development of a large-eddy simulation subgrid model based on artificial neural networks: a case study of turbulent channel flow

Abstract

Abstract. Atmospheric boundary layers and other wall-bounded flows are often simulated with the large-eddy simulation (LES) technique, which relies on subgrid-scale (SGS) models to parameterize the smallest scales. These SGS models often make strong simplifying assumptions. Also, they tend to interact with the discretization errors introduced by the popular LES approach where a staggered finite-volume grid acts as an implicit filter. We therefore developed an alternative LES SGS model based on artificial neural networks (ANNs) for the computational fluid dynamics code MicroHH (v2.0), which can be run in direct numerical simulation (DNS) and LES mode. We used a turbulent channel flow (with a friction Reynolds number Reτ = 590) as a test case. The developed SGS model has been designed to require fewer simplifying assumptions, and to compensate for the instantaneous discretization errors introduced by the staggered finite-volume grid. We trained the ANNs based on instantaneous flow fields from a direct numerical simulation (DNS) of the selected channel flow. In general, we found excellent agreement between the ANN predicted SGS fluxes and the SGS fluxes derived from DNS for flow fields not used during training (with the correlation coefficient ρ mostly varying between 0.6 and 1.0), showing the potential ANNs may have to construct highly accurate SGS models. However, we observed an artificial build-up of turbulence kinetic energy at high wave modes when we directly incorporated our ANN SGS model into a LES simulation of the selected channel flow, eventually resulting in numeric instability. We hypothesized that error accumulation and aliasing errrors, were both important contributors to the observed instability. Several obstacles therefore remain before the a priori promise of our ANN LES SGS model, can be successfully leveraged in practical applications.

Advancing Artificial Neural Network Parameterization for Atmospheric Turbulence Using a Variational Multiscale Model

“…We find two distinct modes of instability, which correspond to the two dimensions of the time march of which our ANNs were unaware during training. First, we observe energy accumulation in the simulation's smallest, resolved scales over several time steps, in similar fashion to what is reported by Beck et al (2019); Brenowitz and Bretherton (2018); Stoffer et al (2020). However, we also see instabilities arise within a time step during corrector passes of the implicit time march.…”

“…In the context of dry, statistically stationary convective boundary layer turbulence, we train and test relatively simple ANN structures outside a time stepping loop (offline), where they promise excellent potential. However, even for such a simple flow, our VMS‐ANN encounters a loss of energy conservation over several time steps in forward simulations of the model problem (an “online” model evaluation setting), similar to that found in studies of similarly simple (e.g., Beck et al., 2019; Stoffer et al., 2020) and more complex (e.g., Brenowitz & Bretherton, 2018; Krasnopolsky et al., 2013) situations. In contrast to those studies, which employed explicit time marches, we investigate the use of an implicit method.…”

“…While this allows the ANN to backscatter energy to the resolved simulation where necessary, there is no enforced control mechanism to maintain the energy in the domain. In other frameworks, similar approaches have resulted in numerical instabilities (Beck et al., 2019; Brenowitz & Bretherton, 2018; Stoffer et al., 2020).…”

“…(2019); Brenowitz and Bretherton (2018); Stoffer et al. (2020). However, we also see instabilities arise within a time step during corrector passes of the implicit time march.…”

“…Over the past few years, several promising flavors of such models have been developed (Duraisamy et al., 2019; Kochkov et al., 2021; Maulik & San, 2017; Yuval & O’Gorman, 2020). Among these flavors, replacing the original parameterization by Artificial Neural Networks (ANNs) appears particularly encouraging for improving the accuracy of both idealized fluid flow calculations (Beck et al., 2019; Guan et al., 2021; Park & Choi, 2021; Stoffer et al., 2020) and global atmospheric models (Brenowitz & Bretherton, 2018; Krasnopolsky et al., 2013; Rasp et al., 2018; Yuval et al., 2021). However, ensuring that an ANN adheres to the laws of physics and returns stable, generalizable simulations remains an appreciable challenge (Gentine et al., 2018).…”