Invariant conservative finite-difference schemes for the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910344516993024 |
|---|---|
| author | Kaptsov, E. I. Dorodnitsyn, V. A. |
| author_facet | Kaptsov, E. I. Dorodnitsyn, V. A. |
| contents | Invariant finite-difference schemes for the one-dimensional shallow water equations in the presence of a magnetic field for various bottom topographies are constructed. Based on the results of the group classification recently carried out by the authors, finite-difference analogues of the conservation laws of the original differential model are obtained. Some typical problems are considered numerically, for which a comparison is made between the cases of a magnetic field presence and when it is absent (the standard shallow water model). The invariance of difference schemes in Lagrangian coordinates and the energy preservation on the obtained numerical solutions are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03488 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Invariant conservative finite-difference schemes for the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates Kaptsov, E. I. Dorodnitsyn, V. A. Numerical Analysis 65M06, 76W05 G.1.8 Invariant finite-difference schemes for the one-dimensional shallow water equations in the presence of a magnetic field for various bottom topographies are constructed. Based on the results of the group classification recently carried out by the authors, finite-difference analogues of the conservation laws of the original differential model are obtained. Some typical problems are considered numerically, for which a comparison is made between the cases of a magnetic field presence and when it is absent (the standard shallow water model). The invariance of difference schemes in Lagrangian coordinates and the energy preservation on the obtained numerical solutions are also discussed. |
| title | Invariant conservative finite-difference schemes for the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates |
| topic | Numerical Analysis 65M06, 76W05 G.1.8 |
| url | https://arxiv.org/abs/2304.03488 |