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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.21948 |
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| _version_ | 1866917319995817984 |
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| author | Liu, Yuchang Guo, Wei Jiang, Yan Zhang, Mengping |
| author_facet | Liu, Yuchang Guo, Wei Jiang, Yan Zhang, Mengping |
| contents | We develop an entropy-stable nodal discontinuous Galerkin (DG) scheme for the Euler equations with gravity, which is also well-balanced with respect to general equilibrium solutions, including both hydrostatic and moving equilibria. The core of our approach lies in a novel treatment of the gravitational source term, combining entropy-conservative numerical fluxes with a linear entropy correction. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structure-preserving nodal DG method for Euler equations with gravity II: general equilibrium states Liu, Yuchang Guo, Wei Jiang, Yan Zhang, Mengping Numerical Analysis We develop an entropy-stable nodal discontinuous Galerkin (DG) scheme for the Euler equations with gravity, which is also well-balanced with respect to general equilibrium solutions, including both hydrostatic and moving equilibria. The core of our approach lies in a novel treatment of the gravitational source term, combining entropy-conservative numerical fluxes with a linear entropy correction. 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. |
| title | Structure-preserving nodal DG method for Euler equations with gravity II: general equilibrium states |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2507.21948 |