Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks
By Shengze Cai, Zhicheng Wang, Frederik Fuest, Y. Jeon, C. Gray, G. Em Karniadakis. Journal of Fluid Mechanics, 2021
344 citations recorded by the source corpus.
Abstract Tomographic background oriented Schlieren (Tomo-BOS) imaging measures density or temperature fields in three dimensions using multiple camera BOS projections, and is particularly useful for instantaneous flow visualizations of complex fluid dynamics problems. We propose a new method based on physics-informed neural networks (PINNs) to infer the full continuous three-dimensional (3-D) velocity and pressure fields from snapshots of 3-D temperature fields obtained by Tomo-BOS imaging. The PINNs seamlessly integrate the underlying physics of the observed fluid flow and the visualization data, hence enabling the inference of latent quantities using limited experimental data. In this hidden fluid mechanics paradigm, we train the neural network by minimizing a loss function composed of a data mismatch term and residual terms associated with the coupled Navier–Stokes and heat transfer equations. We first quantify the accuracy of the proposed method based on a two-dimensional synthetic data set for buoyancy-driven flow, and subsequently apply it to the Tomo-BOS data set, where we are able to infer the instantaneous velocity and pressure fields of the flow over an espresso cup based only on the temperature field provided by the Tomo-BOS imaging. Moreover, we conduct an independent PIV experiment to validate the PINN inference for the unsteady velocity field at a centre plane. To explain the observed flow physics, we also perform systematic PINN simulations at different Reynolds and Richardson numbers and quantify the variations in velocity and pressure fields. The results in this paper indicate that the proposed deep learning technique can become a promising direction in experimental fluid mechanics.
Subfields: Aerospace Engineering, Computational Mechanics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ae1b335f3bd1919b0be4bc20c916b8cc91efdddb
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Citations in the corpus
- Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations (2021, background): “…for example in simulating fluid flow [Raissi et al., 2020, Sun et al., 2020], carrying out cardiac activation mapping [Sahli Costabal et al., 2020], modelling wave physics [Moseley et al., 2020b], and even in predicting the temperature distribution over an espresso cup [Cai et al., 2021].”