A physics-assisted deep neural network-based closure framework for velocity gradient dynamics in compressible flows with vibrational non-equilibrium

In this study, we propose a dynamical model for the evolution of velocity gradients in compressible turbulent flows with vibrational non-equilibrium effects, using physics-assisted deep neural networks.

Such models provide a powerful framework for understanding the nonlinear physics associated with small-scale structures.

In compressible flows, the influence of thermodynamic fields on velocity-gradient dynamics is represented through thermodynamic gradient field (TGF) tensor.

The TGF tensor is one of the primary unclosed terms in velocity-gradient evolution equations.

The TGF tensor comprises contributions from the pressure-Hessian tensor, $\rho\boldsymbol{H}$, and the baroclinic tensor, $\boldsymbol{B}$.

Accordingly, the proposed framework incorporates closures for both $\boldsymbol{H}$ and $\boldsymbol{B}$ tensor dynamics.

Building upon existing phenomenological closures for the $\boldsymbol{H}$ tensor governing mechanisms, we develop a neural-network-based closure for the inviscid mechanism responsible for generating the $\boldsymbol{B}$ tensor.

Unlike the other recently used tensor bases, the presented work employs a novel tensor basis allowing for the inclusion of non-symmetric features in the model.

The framework also incorporates a data-driven closure for vibrational non-equilibrium this http URL resulting framework combines phenomenological and data-driven representations of various $\boldsymbol{H}$ and $\boldsymbol{B}$ tensors governing mechanisms, termed as the \textit{hybrid enhanced homogenized Euler equation} (H-EHEE) model.

Model predictions are evaluated across a range of turbulent Mach numbers and compared against direct numerical simulation (DNS) data and existing compressible velocity-gradient models.

The H-EHEE model exhibits close agreement with DNS statistics and provides significant improvements over existing models, particularly in highly compressible flow regimes.