Extraction of Moment Closures for Strongly Non-Equilibrium Flows via Machine Learning

TL;DR

This work bridges machine learning with continuum mechanics, offering a road map for high-fidelity aerothermal predictions in next-generation supersonic vehicles.

Abstract

We introduce a machine learning framework for moment-equation modeling of rarefied gas flows, addressing strongly non-equilibrium conditions inaccessible to conventional computational fluid dynamics. Our approach utilizes high-order moments and collision integrals, highly sensitive to non-equilibrium effects, as key predictive variables. Training datasets are created from one-dimensional steady shock simulations, and a methodology of computing collision integrals is developed. By learning thermodynamically consistent closures directly from DSMC data, our R13-ML model, combined with a discontinuous Galerkin solver for the transfer equations of moments, preserves physical structure and accurately predicts normal shock structures and generalizes to hypersonic and some unsteady, one-dimensional wave scenarios. This work bridges machine learning with continuum mechanics, offering a road map for high-fidelity aerothermal predictions in next-generation supersonic vehicles.

Figures (4)

• Figure 1: Overview of the R13-ML-model based on an FCNN with offline training and physics-based online computation github_R13ML
• Figure 2: Performance of the R13-ML model on test data: Moment dependencies in 1D shocks at $\text{Ma}=3,5,7$
• Figure 3: One-dimensional shock structure problem: solution comparison for normalized stress ($\sigma$) and normalized heat flux ($q$) at $\text{Ma}=5, 7, 9$. Excellent agreement also for $\text{Ma}=9$, which is outside the trainings set.
• Figure 4: Simulation of unsteady flow: (a) two shock interaction at $t=22.830\tau_0$ after the collision of two shock waves. (b) shock-high temperature region interaction at $t=7.610\tau_0$ after impingement of a stream on a high temperature region.