Investigating Machine Learning-Based Shock Sensors for Scale-Resolving Discontinuous Galerkin Simulations
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In the presence of flow discontinuities, high-order methods suffer from spurious oscillations, which compromise the accuracy and robustness of simulations. In this context, we explore the use of neural network-based shock detectors to sharply introduce artificial viscosity in an entropy-stable modal discontinuous Galerkin (dG) discretization of the fluid dynamics equations [1]. Two families of detectors are investigated. The first follows the approach proposed in [2] and [3], leveraging nodal values of the solution; the second directly uses the coefficients of the polynomial modal expansion. The performance is assessed through a series of benchmark cases, including 1D and 2D Riemann problems. As a 3D flow case, we consider the Taylor–Green Vortex (TGV) at Mach 1.25, a configuration of particular interest due to the complex interplay between shocks and turbulence [4]. REFERENCES [1] L. Alberti et al., ”A comparative study of different sets of variables in a Discontinuous Galerkin Method with Entropy Balance Enforcement, Int. J. Comput. Fluid Dyn., 2024. [2] A. D. Beck et al., “A neural network based shock detection and localization approach for discontinuous Galerkin methods,” Journal of Computational Physics, 2020. [3] D. Ray and J. S. Hesthaven, “An artificial neural network as a troubled-cell indicator,” Journal of Computational Physics, 2018. [4] D. J. Lusher and N. D. Sandham, “Assessment of low-dissipative shock-capturing schemes for the compressible Taylor–Green Vortex,” AIAA Journal, 2021.