Deep learning closure models for large-eddy simulation of flows around bluff bodies

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 (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 training situ incompressible around rectangular prisms at moderate Reynolds numbers. The DL-LES models trained using adjoint partial differential equation (PDE) optimization methods to match, as closely possible, direct numerical (DNS) data. They then evaluated out-of-sample – aspect ratios, numbers bluff-body geometries not included data compared with standard models. outperform these able achieve accurate on relatively coarse (downsampled from DNS factors four or eight each Cartesian direction). We study accuracy predicting drag coefficient, far-field mean flow, resolved stress. crucial that quantities interest steady-state statistics; example, 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 statistics therefore requires simulating over large number times through domain. It non-trivial question whether an unsteady PDE functional form defined network remain stable $t \in [0, )$ , especially when comparatively short time intervals. Our results demonstrate long horizons, which enables estimation velocity, fluctuations coefficient turbulent bluff bodies relevant applications.