Kinetic data-driven approach to turbulence subgrid modeling

Abstract

Numerical simulations of turbulent flows are well known to pose extreme computational challenges due to the huge number of dynamical degrees of freedom required to correctly describe the complex multi-scale statistical correlations of the velocity. On the other hand, kinetic mesoscale approaches based on the Boltzmann equation, have the potential to describe a broad range of flows, stretching well beyond the special case of gases close to equilibrium, which results in the ordinary Navier-Stokes dynamics. Here we demonstrate that, by properly tuning, a kinetic approach can statistically reproduce the quantitative dynamics of the larger scales in turbulence, thereby providing an alternative, computationally efficient and physically rooted approach towards subgrid scale (SGS) modeling in turbulence. More specifically we show that by leveraging on data from fully resolved Direct Numerical Simulation (DNS) we can learn a collision operator for the discretized Boltzmann equation solver (the lattice Boltzmann method), which effectively implies a turbulence subgrid closure model. The mesoscopic nature of our formulation makes the learning problem fully local in both space and time, leading to reduced computational costs and enhanced generalization capabilities. We show that the model offers superior performance compared to traditional methods, such as the Smagorinsky model, being less dissipative and, therefore, being able to more closely capture the intermittency of higher-order velocity correlations. This foundational work lays the basis for extending the proposed framework to different turbulent flow settings and -- most importantly -- to develop new classes of hybrid data-driven kinetic-based models capable of faithfully capturing the complex macroscopic dynamics of diverse physical systems such as emulsions, non-Newtonian fluid and multiphase systems.