Lattice Boltzmann method with artificial bulk viscosity using a neural collision operator

The lattice Boltzmann method (lbm) stands apart from conventional macroscopic approaches due to its low numerical dissipation and reduced computational cost, attributed to a simple streaming and local collision step. While this property makes the method particularly attractive for applications such as direct noise computation, it also renders the method highly susceptible to instabilities. A vast body of literature exists on stability-enhancing techniques, which can be categorized into selective filtering, regularized lbm, and multi-relaxation time (mrt) models. Although each technique bolsters stability by adding numerical dissipation, they act on different modes. Consequently, there isn't a universal scheme optimally suited for a wide range of different flows. The reason for this lies in the static nature of these methods; they cannot adapt to local or global flow features. Still, adaptive filtering using a shear sensor constitutes an exception to this. For this reason, we developed a novel collision operator that uses space- and time-variant collision rates associated with the bulk viscosity. These rates are optimized by a physically informed neural net. In this study, the training data consists of a time series of different instances of a 2D barotropic vortex solution, obtained from a high-order Navier–Stokes solver that embodies desirable numerical features. For this specific text case our results demonstrate that the relaxation times adapt to the local flow and show a dependence on the velocity field. Furthermore, the novel collision operator demonstrates a better stability-to-precision ratio and outperforms conventional techniques that use an empirical constant for the bulk viscosity.