Modeling of vibrational nonequilibrium effects on pressure Hessian tensor using physics-assisted deep neural networks

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This study focuses on modeling the effect of vibrational nonequilibrium on the pressure Hessian tensor. The pressure Hessian tensor is one of the unclosed processes involved in the velocity gradient evolution equation. Accessing the velocity gradient tensor following a fluid particle is needed to understand the physics of various nonlinear turbulent processes. Our modeling strategy employs a combination of two different deep neural networks (DNNs) to model the magnitude and the directional aspects of the vibrational nonequilibrium tensor separately. Both the DNNs are optimized using two appropriate physics-assisted custom loss functions, comparing the desired features of the DNN predictions against the exact behavior observed in the direct numerical simulation (DNS) database. A detailed investigation of four different DNS databases of vibrationally excited decaying compressible turbulence with different initial Reynolds numbers, Mach numbers, and vibrational Damköhler numbers is performed to identify the appropriate normalized forms of input and output quantities for the two neural networks. The training of both the DNNs is done using the DNS data of merely one simulation. The trained models are then subjected to extensive evaluation against different DNS databases. Indeed, the new model captures many DNS features quite well. Such an extensive evaluation of the new model proves the generalizability of the model, at least in the range of parameters involved in our study.