@article {wan2020a,
	title = {Bubbles in turbulent flows: Data-driven, kinematic models with history terms},
	journal = {Int. J. Multiphas. Flow},
	volume = {129},
	year = {2020},
	month = {aug},
	pages = {103286},
	publisher = {Elsevier BV},
	abstract = {We present data driven kinematic models for the motion of bubbles in high-Re turbulent fluid flows based on recurrent neural networks with long-short term memory enhancements. The models extend empirical relations, such as Maxey-Riley (MR) and its variants, whose applicability is limited when either the bubble size is large or the flow is very complex. The recurrent neural networks are trained on the trajectories of bubbles obtained by Direct Numerical Simulations (DNS) of the Navier Stokes equations for a two-component incompressible flow model. Long short term memory components exploit the time history of the flow field that the bubbles have encountered along their trajectories and the networks are further augmented by imposing rotational invariance to their structure. We first train and validate the formulated model using DNS data for a turbulent Taylor-Green vortex. Then we examine the model pre- dictive capabilities and its generalization to Reynolds numbers that are different from those of the train- ing data on benchmark problems, including a steady (Hill{\textquoteright}s spherical vortex) and an unsteady (Gaussian vortex ring) flow field. We find that the predictions of the developed model are significantly improved compared with those obtained by the MR equation. Our results indicate that data-driven models with history terms are well suited in capturing the trajectories of bubbles in turbulent flows.},
	doi = {10.1016/j.ijmultiphaseflow.2020.103286},
	url = {https://cse-lab.seas.harvard.edu/files/cse-lab/files/wan2020a.pdf},
	author = {Wan, Zhong Yi and Karnakov, Petr and Koumoutsakos, Petros and Themistoklis P. Sapsis}
}
