Entropy Stable DGSEM Schemes of Gauss Points Based on Subcell Limiting

Area of Science:

• Computational Fluid Dynamics
• Numerical Analysis
• High-Performance Computing

Background:

• The discontinuous Galerkin spectral element method (DGSEM) offers high-order accuracy on complex meshes.
• Aliasing errors and non-physical oscillations can compromise DGSEM stability in simulations of vortex flows and shock waves.

Purpose of the Study:

• To develop a more non-linearly stable and robust DGSEM.
• To address limitations of standard DGSEM in simulating challenging fluid dynamics phenomena.

Main Methods:

• Introduction of an entropy-stable DGSEM (ESDGSEM) incorporating subcell limiting.
• Analysis of stability and resolution properties of ESDGSEM at different solution points.
• Establishment of a provably entropy-stable DGSEM with subcell limiting on Legendre-Gauss (LG) points.

Main Results:

• The proposed ESDGSEM demonstrates superior non-linear stability and resolution compared to standard DGSEM.
• The subcell limiting technique significantly enhances the robustness of the ESDGSEM-LG scheme for shock-capturing.

Conclusions:

• The entropy-stable DGSEM with subcell limiting provides a robust and accurate numerical method for complex fluid flow simulations.
• The ESDGSEM-LG scheme is particularly effective for problems involving under-resolved vortices and shock waves.