| Abstract: |
| We propose an entropy stable and well-balanced discontinuous Galerkin (DG) scheme for the Euler equations with gravity To achieve these properties, we utilize the nodal DG framework and carefully design the source term discretization using entropy conservative fluxes. In addition, the proposed formulation is carefully designed to ensure compatibility with a positivity-preserving limiter. We provide a rigorous theoretical analysis to establish the accuracy and structure- preserving properties of the proposed scheme. Extensive numerical experiments confirm the robustness and efficiency of the scheme. |
|