Fast neural network-based direct simulation Monte Carlo solutions of shock flow of diatomic gases with vibrational modes

Abstract

A novel way to solve gas flows in thermal non-equilibrium has been proposed by Garg et al. [Phys. Fluids 36, 106113 (2024)], which built compact constitutive relations (CR) for monatomic gases in advance by applying deep neural network (DNN) machine learning (ML) to available direct simulation Monte Carlo (DSMC) solution data and later combined them with the conventional finite volume method (FVM) for the physical laws of conservation. We extend this FVM-DSMC-ML framework to diatomic gases by employing the two-temperature framework (translational and rotational) as well as the three-temperature framework (translational, rotational, and vibrational), coupled with DNN-based DSMC CRs for viscous stress and heat fluxes associated with these energy modes. After resolving challenges associated with various energy modes, we evaluate the performance of the FVM-DSMC-ML solver for diatomic gases for the compressive shock structure problem. Developing a successful DNN model requires the careful selection of input and output parameters, as well as meticulous attention to the details of various DNN parameters. The DNN model of DSMC CRs is trained using filtered data as inputs, with corresponding DSMC data as outputs. The study demonstrates that the FVM-DSMC-ML solver provides results in excellent agreement with the actual DSMC solutions and shows superior performance, with its computational cost being 1/50th of that of the conventional DSMC solver. The DSMC topologies reveal pronounced nonlinearities and strong coupling between viscous stress and heat fluxes and for the most part they exhibit higher values of viscous stress and heat fluxes compared to the Navier-Stokes and Fourier topology.