An unsupervised machine-learning-based shock sensor for high-order supersonic flow solvers

TL;DR

This paper introduces an unsupervised Gaussian Mixture Model-based shock sensor that accurately detects shocks in high-order supersonic flow simulations, enhancing stability and robustness with minimal parameter tuning.

Contribution

The novel GMM-based shock sensor offers improved accuracy and robustness over existing methods, requiring less parameter tuning and suitable for complex geometries and diverse flow conditions.

Findings

GMM sensor outperforms state-of-the-art alternatives in shock detection.

Sensor enhances hybrid stabilization methods in high-order solvers.

Effective in high Reynolds number supersonic flows.

Abstract

We present a novel unsupervised machine-learning sock sensor based on Gaussian Mixture Models (GMMs). The proposed GMM sensor demonstrates remarkable accuracy in detecting shocks and is robust across diverse test cases with significantly less parameter tuning than other options. We compare the GMM-based sensor with state-of-the-art alternatives. All methods are integrated into a high-order compressible discontinuous Galerkin solver, where two stabilization approaches are coupled to the sensor to provide examples of possible applications. The Sedov blast and double Mach reflection cases demonstrate that our proposed sensor can enhance hybrid sub-cell flux-differencing formulations by providing accurate information of the nodes that require low-order blending. Besides, supersonic test cases including high Reynolds numbers showcase the sensor performance when used to introduce entropy-stable artificial viscosity to capture shocks, demonstrating the same effectiveness as fine-tuned state-of-the-art sensors. The adaptive nature and ability to function without extensive training datasets make this GMM-based sensor suitable for complex geometries and varied flow configurations. Our study reveals the potential of unsupervised machine-learning methods, exemplified by this GMM sensor, to improve the robustness and efficiency of advanced CFD codes.