In this work, we propose using an ensemble Kalman method to learn a nonlinear eddy viscosity model, represented as a tensor basis neural network, from velocity data. Data-driven turbulence models have emerged as a promising alternative to traditional models for providing closure mapping from the mean velocities to Reynolds stresses. Most data-driven models in this category need full-field Reynolds stress data for training, which not only places stringent demand on the data generation but also makes the trained model ill-conditioned and lacks robustness. This difficulty can be alleviated by incorporating the Reynolds-averaged Navier–Stokes (RANS) solver in the training process. However, this would necessitate developing adjoint solvers of the RANS model, which requires extra effort in code development and maintenance. Given this difficulty, we present an ensemble Kalman method with an adaptive step size to train a neural-network-based turbulence model by using indirect observation data. To our knowledge, this is the first such attempt in turbulence modelling. The ensemble method is first verified on the flow in a square duct, where it correctly learns the underlying turbulence models from velocity data. Then the generalizability of the learned model is evaluated on a family of separated flows over periodic hills. It is demonstrated that the turbulence model learned in one flow can predict flows in similar configurations with varying slopes.

The dispersion of viral droplets plays a key role in the transmission of COVID-19. In this work, we analyze the dispersion of cough-generated droplets in the wake of a walking person for different space sizes. The air flow is simulated by solving the Reynolds-averaged Navier–Stokes equations, and the droplets are modeled as passive Lagrangian particles. Simulation results show that the cloud of droplets locates around and below the waist height of the manikin after 2 s from coughing, which indicates that kids walking behind an infectious patient are exposed to higher transmission risk than adults. More importantly, two distinct droplet dispersion modes occupying significantly different contamination regions are discovered. A slight change of space size is found being able to trigger the transition of dispersion modes even though the flow patterns are still similar. This shows the importance of accurately simulating the air flow in predicting the dispersion of viral droplets and implies the necessity to set different safe-distancing guidelines for different environments.