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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2605.17132 |
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| _version_ | 1866911691688640512 |
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| author | Mantilla, Andrés Mauricio Suárez Colorado, Leonardo Castañeda |
| author_facet | Mantilla, Andrés Mauricio Suárez Colorado, Leonardo Castañeda |
| contents | We describe a high-order ADER-DG solver for the compressible Euler equations within the ExaHyPE framework. The implementation combines a high-order ADER-DG polynomial representation, a local space-time DG predictor, adaptive mesh refinement, and an a posteriori subcell finite-volume limiter. We test the code on a deliberately mixed set of one- and two-dimensional problems: a strong-shock Sod-type problem, the Shu-Osher shock-entropy interaction, the Woodward-Colella blast wave, a contact-driven vortex sheet, and a shock-interface interaction. The one-dimensional cases recover the expected Euler wave patterns and show clear order-dependent gains in smooth and oscillatory regions. The two-dimensional cases probe a different part of the method, namely contact preservation, shear-driven roll-up, baroclinic vorticity deposition, and Richtmyer-Meshkov-type growth. In these tests the high-order update gives the expected resolution away from discontinuities, whereas the subcell limiter keeps the calculation stable near shocks and steep interfaces. The resulting code provides a reproducible ExaHyPE implementation for idealised inviscid, non-relativistic flows in which shocks, contacts, and multidimensional interfaces are the dominant features. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17132 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | High-Order ADER-DG Hydrodynamics with ExaHyPE: Implementation, Validation, and Astrophysical Benchmarking Mantilla, Andrés Mauricio Suárez Colorado, Leonardo Castañeda Fluid Dynamics Computational Physics 76M12, 76N15, 65M60, 65M08 We describe a high-order ADER-DG solver for the compressible Euler equations within the ExaHyPE framework. The implementation combines a high-order ADER-DG polynomial representation, a local space-time DG predictor, adaptive mesh refinement, and an a posteriori subcell finite-volume limiter. We test the code on a deliberately mixed set of one- and two-dimensional problems: a strong-shock Sod-type problem, the Shu-Osher shock-entropy interaction, the Woodward-Colella blast wave, a contact-driven vortex sheet, and a shock-interface interaction. The one-dimensional cases recover the expected Euler wave patterns and show clear order-dependent gains in smooth and oscillatory regions. The two-dimensional cases probe a different part of the method, namely contact preservation, shear-driven roll-up, baroclinic vorticity deposition, and Richtmyer-Meshkov-type growth. In these tests the high-order update gives the expected resolution away from discontinuities, whereas the subcell limiter keeps the calculation stable near shocks and steep interfaces. The resulting code provides a reproducible ExaHyPE implementation for idealised inviscid, non-relativistic flows in which shocks, contacts, and multidimensional interfaces are the dominant features. |
| title | High-Order ADER-DG Hydrodynamics with ExaHyPE: Implementation, Validation, and Astrophysical Benchmarking |
| topic | Fluid Dynamics Computational Physics 76M12, 76N15, 65M60, 65M08 |
| url | https://arxiv.org/abs/2605.17132 |