A Characteristic Mapping Method with Source Terms: Applications to Ideal Magnetohydrodynamics
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914345033662464 |
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| author | Yin, Xi-Yuan Krah, Philipp Nave, Jean-Christophe Schneider, Kai |
| author_facet | Yin, Xi-Yuan Krah, Philipp Nave, Jean-Christophe Schneider, Kai |
| contents | This work introduces a generalized characteristic mapping method designed to handle non-linear advection with source terms. The semi-Lagrangian approach advances the flow map, incorporating the source term via the Duhamel integral. We derive a recursive formula for the time decomposition of the map and the source term integral, enhancing computational efficiency. Benchmark computations are presented for a test case with an exact solution and for two-dimensional ideal incompressible magnetohydrodynamics (MHD). Results demonstrate third-order accuracy in both space and time. The submap decomposition method achieves exceptionally high resolution, as illustrated by zooming into fine-scale current sheets. An error estimate is performed and suggests third order convergence in space and time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13772 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Characteristic Mapping Method with Source Terms: Applications to Ideal Magnetohydrodynamics Yin, Xi-Yuan Krah, Philipp Nave, Jean-Christophe Schneider, Kai Numerical Analysis Computational Physics Fluid Dynamics Plasma Physics This work introduces a generalized characteristic mapping method designed to handle non-linear advection with source terms. The semi-Lagrangian approach advances the flow map, incorporating the source term via the Duhamel integral. We derive a recursive formula for the time decomposition of the map and the source term integral, enhancing computational efficiency. Benchmark computations are presented for a test case with an exact solution and for two-dimensional ideal incompressible magnetohydrodynamics (MHD). Results demonstrate third-order accuracy in both space and time. The submap decomposition method achieves exceptionally high resolution, as illustrated by zooming into fine-scale current sheets. An error estimate is performed and suggests third order convergence in space and time. |
| title | A Characteristic Mapping Method with Source Terms: Applications to Ideal Magnetohydrodynamics |
| topic | Numerical Analysis Computational Physics Fluid Dynamics Plasma Physics |
| url | https://arxiv.org/abs/2411.13772 |