Entropy correction artificial viscosity for high order DG methods using multiple artificial viscosities

Entropy stable discontinuous Galerkin (DG) methods display improved robustness for problems with shocks, turbulence, and under-resolved features by enforcing an entropy inequality. Such methods have traditionally relied on entropy conservative (EC) fluxes that are computationally expensive to evaluate. An alternative approach for enforcing an entropy inequality is through a minimally dissipative ``entropy correction" artificial viscosity. We review how to construct such an artificial viscosity formulation and extend this approach to multiple types of viscosity (e.g., viscosity and thermal diffusivity). We determine simple analytical expressions for optimal viscosity parameters. We compare this to the case of a single monolithic viscosity parameter for different 1D and 2D problems, and show that the proposed method allows users to more precisely target specific physical phenomena while retaining robustness for general problem settings.

Source: arXiv:2604.03158v1 - http://arxiv.org/abs/2604.03158v1 PDF: https://arxiv.org/pdf/2604.03158v1 Original Link: http://arxiv.org/abs/2604.03158v1