Towards Efficient Simulations of Non-Equilibrium Chemistry in Hypersonic Flows: Application of Neural Operators in Multidimensional CFD Simulations

This work introduces further developments in designing a novel numerical framework to address the challenges in solving computationally intensive but physically accurate thermochemical non-equilibrium models for high-speed flows. The primary objective of this study is to conduct a preliminary assessment of the computational performance and accuracy of neural operator-based surrogate modeling for chemistry within computational fluid dynamics (CFD) environments, particularly in multidimensional configurations. The proposed framework employs operator-splitting time integrators to decompose the governing equations into more tractable transport and reaction operators, each treated using its optimal integration scheme. Within this framework, the integration of the stiff reaction operator, typically handled by implicit methods, is replaced by a fast evaluation of a machine learning-based surrogate trained via zero-dimensional simulations, making it geometry-independent and applicable to configurations of any dimension (1D, 2D, or 3D). A specific neural operator architecture is employed to construct the surrogate, providing advantages in resolution invariance and generalizability over traditional deep neural networks. The study conducts numerical experiments on two 2D geometries, namely a quarter of a sphere and the Apollo shield. The results highlight the promising potential of the proposed framework, demonstrating its capability to accurately recover steady-state solutions with a relative error below 2.4% for quantities of interest, along with a speedup of X2.6.