The accurate treatment of outflow boundary conditions remains a critical challenge in computational fluid dynamics when predicting aerodynamic forces and/or acoustic emissions. This is particularly evident when employing the lattice Boltzmann method (LBM) as the numerical solution technique, which often suffers from inaccuracies induced by artificial reflections from outflow boundaries. This paper investigates the use of neural networks to mitigate these adverse boundary effects and enable truncated domain requirements. Two distinct NN-based approaches are proposed: (1) direct reconstruction of unknown particle distribution functions at the outflow boundary; and (2) enhancement of established characteristic boundary conditions by dynamically tuning their parameters. The direct reconstruction model was trained on data generated from a two-dimensional (2D) flow over a cylindrical obstruction. The drag, lift, and Strouhal number were used to test the new boundary condition. We analyzed results for various Reynolds numbers and restricted domain sizes, where it demonstrated significantly improved predictions when compared with the traditional Zou and He boundary condition. To examine the robustness of the NN-based reconstruction, the same condition was applied to the simulation of a National Advisory Committee for Aeronautics 0012 airfoil, again providing accurate aerodynamic performance predictions. The neural-enhanced characteristic boundary condition (CBC) was evaluated on a 2D convected vortex benchmark and showed superior performance in minimizing density errors compared to CBCs with fixed parameters. These findings highlight the potential of NN-integrated boundary conditions to improve accuracy and reduce computational expense of aerodynamic and acoustic emission simulations with the LBM.
Bedrunka et al. (Thu,) studied this question.