Machine learning-accelerated computational non-equilibrium flow: Deep neural network prediction of transport properties

The characterization of non-equilibrium transport phenomena plays an essential role in modeling many fluid flow processes, such as high-speed shocks, flame propagation, and plasma flow. The Boltzmann perturbation method, originating from microscopic particle collisions, effectively captures transport properties within fluids. However, under non-equilibrium conditions, the computational cost of coupling iterative solvers for transport properties in computational fluid dynamics becomes prohibitively high, leading to an unfavorable trade-off between accuracy and tractability. To overcome this challenge, we employ a deep neural network in this work to replace the Boltzmann perturbation method for obtaining transport properties in high-speed air non-equilibrium flows, enabling accelerated computations for non-equilibrium flow. For simulating non-equilibrium airflow around hypersonic vehicles, our method achieves comparable accuracy to the Boltzmann perturbation method, with average errors in transport properties below 0.5%. Compared to the conventional iterative coupling approach, the deep neural network eliminates the need for solving collision parameters between particles and Sonine polynomials, resulting in a 50- to 70-fold computational speedup. Furthermore, the neural network demonstrates excellent generalization capabilities for other flight geometries and conditions. Our approach exemplifies how computational fluid dynamics can leverage machine learning from the perspective of fluid physical properties to improve simulations.