A new class of entropy stable fluctuations for the discontinuous Galerkin method with application to the Saint-Venant-Exner model
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911376182607872 |
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| author | Ersing, Patrick Winters, Andrew R. |
| author_facet | Ersing, Patrick Winters, Andrew R. |
| contents | In this work we consider entropy stable discontinuous Galerkin methods applied to nonconservative hyperbolic systems. We introduce a new class of entropy conservative fluctuations that allow us to construct entropy conservative schemes without any system-specific derivations. We demonstrate that a loss of entropy symmetrization for nonconservative systems restricts the design of entropy stable fluctuations and propose a novel blending procedure to construct entropy stable dissipation terms from general numerical viscosity matrices. The resulting methodology is applied to develop a high-order, entropy stable, and well-balanced approximation for the Saint-Venant-Exner system. Numerical tests are presented to verify the theoretical findings and demonstrate the performance and robustness of the proposed scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09450 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A new class of entropy stable fluctuations for the discontinuous Galerkin method with application to the Saint-Venant-Exner model Ersing, Patrick Winters, Andrew R. Numerical Analysis 65M70, 65M12, 65M20, 76M22 In this work we consider entropy stable discontinuous Galerkin methods applied to nonconservative hyperbolic systems. We introduce a new class of entropy conservative fluctuations that allow us to construct entropy conservative schemes without any system-specific derivations. We demonstrate that a loss of entropy symmetrization for nonconservative systems restricts the design of entropy stable fluctuations and propose a novel blending procedure to construct entropy stable dissipation terms from general numerical viscosity matrices. The resulting methodology is applied to develop a high-order, entropy stable, and well-balanced approximation for the Saint-Venant-Exner system. Numerical tests are presented to verify the theoretical findings and demonstrate the performance and robustness of the proposed scheme. |
| title | A new class of entropy stable fluctuations for the discontinuous Galerkin method with application to the Saint-Venant-Exner model |
| topic | Numerical Analysis 65M70, 65M12, 65M20, 76M22 |
| url | https://arxiv.org/abs/2601.09450 |