Near-wall flow simulation remains a central challenge in aerodynamics modelling: Reynolds-averaged Navier–Stokes predictions of separated flows are often inaccurate, and large-eddy simulation (LES) can require prohibitively small near-wall mesh sizes. A deep learning (DL) closure model for LES is developed by introducing untrained neural networks into the governing equations and training in situ for incompressible flows around rectangular prisms at moderate Reynolds numbers. The DL-LES models are trained using adjoint partial differential equation (PDE) optimization methods to match, as closely as possible, direct numerical simulation (DNS) data. They are then evaluated out-of-sample – for aspect ratios, Reynolds numbers and bluff-body geometries not included in the training data – and compared with standard LES models. The DL-LES models outperform these models and are able to achieve accurate LES predictions on a relatively coarse mesh (downsampled from the DNS mesh by factors of four or eight in each Cartesian direction). We study the accuracy of the DL-LES model for predicting the drag coefficient, near-wall and far-field mean flow, and resolved Reynolds stress. A crucial challenge is that the LES quantities of interest are the steady-state flow statistics; for example, a time-averaged velocity component $\langle {u}_i\rangle (x) = \lim _{t \rightarrow \infty } ({1}/{t}) \int _0^t u_i(s,x)\, {\rm d}s$ . Calculating the steady-state flow statistics therefore requires simulating the DL-LES equations over a large number of flow times through the domain. It is a non-trivial question whether an unsteady PDE model with a functional form defined by a deep neural network can remain stable and accurate on $t \in [0, \infty )$ , especially when trained over comparatively short time intervals. Our results demonstrate that the DL-LES models are accurate and stable over long time horizons, which enables the estimation of the steady-state mean velocity, fluctuations and drag coefficient of turbulent flows around bluff bodies relevant to aerodynamics applications.
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Data‐Driven Prediction of Turbulent Flow Statistics Past Bridge Piers in Large‐Scale Rivers Using Convolutional Neural Networks
Prediction of statistical properties of the turbulent flow in large‐scale rivers is essential for river flow analysis. The large‐eddy simulation (LES) provides a powerful tool for such predictions; however, it requires a very long sampling time and demands significant computing power to calculate the turbulence statistics of riverine flows. In this study, we developed encoder‐decoder convolutional neural networks (CNNs) to predict the first‐ and second‐order turbulence statistics of the turbulent flow of large‐scale meandering rivers using instantaneous LES results. We train the CNNs using a data set obtained from LES of the flood flow in a large‐scale river with three bridge piers—a training testbed. Subsequently, we employed the trained CNNs to predict the turbulence statistics of the flood flow in two different meandering rivers and bridge pier arrangements—validation testbed rivers. The CNN predictions for the validation testbed river flow were compared with the simulation results of a separately done LES to evaluate the performance of the developed CNNs. We show that the trained CNNs can successfully produce turbulence statistics of the flood flow in the large‐scale rivers, that is, the validation testbeds.
more » « less- Award ID(s):
- 1823530
- NSF-PAR ID:
- 10445078
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Water Resources Research
- Volume:
- 58
- Issue:
- 1
- ISSN:
- 0043-1397
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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