Neural stochastic differential equations for particle dispersion in large-eddy simulations of homogeneous isotropic turbulence

Abstract

In dilute turbulent particle-laden flows, such as atmospheric dispersion of pollutants or virus particles, the dynamics of tracer-like to low inertial particles are significantly altered by the fluctuating motion of the carrier fluid phase. Neglecting the effects of fluid velocity fluctuations on particle dynamics causes poor prediction of particle transport and dispersion. To account for the effects of fluid phase fluctuating velocity on the particle transport, stochastic differential equations coupled with large eddy simulation are proposed to model the fluid velocity seen by the particle. The drift and diffusion terms in the stochastic differential equation are modelled using neural networks ('neural stochastic differential equations'). The neural networks are trained with direct numerical simulations (DNS) of decaying homogeneous isotropic turbulence at low and moderate Reynolds numbers. The predictability of the proposed models are assessed through a priori analyses and a posteriori simulations of decaying homogeneous isotropic turbulence at low-to-high Reynolds numbers. Total particle fluctuating kinetic energy are under-predicted by 40% with no model, compared to the DNS data. In contrast, the proposed model predictions match total particle fluctuating kinetic energy to within 5% of the DNS data for low to high-inertia particles. For inertial particles, the model matches the variance of uncorrelated particle velocity to within 10% of DNS results, compared to 60-70% under-prediction with no model. It is concluded that the proposed mathematical and computational framework is applicable for flow configurations involving tracer and inertial particles, such as transport and dispersion of pollutants or virus particles.

Validated respiratory drug deposition predictions from 2D and 3D medical images with statistical shape models and convolutional neural networks

“…As described in [7], our computational fluid dynamics mesh had a spacing of Δ = 500 μm, which gave excellent agreement with flow through 3D printed airways [92]. The fluid turbulence modelling is discussed in detail in [96]. Particles were tracked in a Lagrangian approach by solving Newton's equations of motion accounting for drag and gravity, as we showed in our previous study that particle-particle interactions are not influential [7].…”