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The lattice Boltzmann method (LBM) is an efficient simulation technique for computational fluid mechanics and beyond. It is based on a simple stream-and-collide algorithm on Cartesian grids, which is easily compatible with modern machine learning architectures. While it is becoming increasingly clear that deep learning can provide a decisive stimulus for classical simulation techniques, recent studies have not addressed possible connections between machine learning and LBM. Here, we introduce Lettuce, a PyTorch-based LBM code with a threefold aim. Lettuce enables GPU accelerated calculations with minimal source code, facilitates rapid prototyping of LBM models, and enables integrating LBM simulations with PyTorch’s deep learning and automatic differentiation facility. As a proof of concept for combining machine learning with the LBM, a neural collision model is developed, trained on a doubly periodic shear layer and then transferred to a different flow, a decaying turbulence. We also exemplify the added benefit of PyTorch’s automatic differentiation framework in flow control and optimization. To this end, the spectrum of a forced isotropic turbulence is maintained without further constraining the velocity field. The source code is freely available from https://github.com/lettucecfd/lettuce.

A far-field solver based on the acoustic analogy of Ffowcs Williams and Hawkings for acoustic problems with convection and vortical waves was implemented in the open source package Overture. The numerical calculations of CAA test cases showed good agreement with analytical solutions or results from measurements and simulation data from the literature. This paper presents the implemented solver and its verification. In futher work, the developed framework will be used to investigate jet-flap interaction and the emitted sound field, numerically.

A round jet with \(Re=3600\) and \(M=0.9\) as well as two planar nozzle-wing flap configurations were simulated by using LES. An evaluation was proposed to predict the effect of the instantaneous Lighthill sources, S, their linear components, \(S^{\mathrm {l}}\), and non-linear components, \(S^{\mathrm {n}}\). The simulations indicate that conclusions can be made regarding the directional characteristic of the emitted sound field. These findings were used in investigations of a nozzle-wing-flap configuration. The wing-nozzle configuration showed increased values of the mean Lighthill source terms on the bottom of the wing and flap, contrary to the case of an isolated wing.

Coaxial jets originating from a nozzle interacting with a two-element wing configuration consisting of a main wing and a flap are computed using large-eddy simulations (LES) to investigate in the long term the effect of the interaction on the sound field of this jet-wing-flap configuration. The secondary jet Mach number is \(M_s=0.37\) and the Reynolds number based on the secondary velocity and diameter is \(Re_{s}=1.32 \times 10^6\). The nozzle inlet boundary layers are modeled by Blasius velocity profiles with a boundary layer thicknesses of 20% of the nozzle channel half-width. The acoustic far-field is predicted by solving the linearized Euler equations (LEE) in a region attached to the LES domain. The jet streams interacts with the two-element wing configuration and lead to a significantly changed mean flow field in the wing-flap gap area and pressure at the wing surface. Additionally, a strong influence of the flap on the jet development is observed, especially in the case of a non-zero free stream velocity.