Bound Preserving Lax-Wendroff Flux Reconstruction Method for Special Relativistic Hydrodynamics
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910813013409792 |
|---|---|
| author | Basak, Sujoy Babbar, Arpit Kumar, Harish Chandrashekar, Praveen |
| author_facet | Basak, Sujoy Babbar, Arpit Kumar, Harish Chandrashekar, Praveen |
| contents | Lax-Wendroff flux reconstruction (LWFR) schemes have high order of accuracy in both space and time despite having a single internal time step. Here, we design a Jacobian-free LWFR type scheme to solve the special relativistic hydrodynamics equations on Cartesian grids. We then blend the scheme with a first-order finite volume scheme to control the oscillations near discontinuities. We also use a scaling limiter to preserve the physical admissibility of the solution after ensuring the scheme is admissible in means. A particular focus is given to designing a discontinuity indicator model to detect the local non-smoothness in the solution of the highly non-linear relativistic hydrodynamics equations. Finally, we present numerical results for a wide range of test cases to show the robustness and efficiency of the proposed scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15805 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bound Preserving Lax-Wendroff Flux Reconstruction Method for Special Relativistic Hydrodynamics Basak, Sujoy Babbar, Arpit Kumar, Harish Chandrashekar, Praveen Numerical Analysis 65M60 G.1.8 Lax-Wendroff flux reconstruction (LWFR) schemes have high order of accuracy in both space and time despite having a single internal time step. Here, we design a Jacobian-free LWFR type scheme to solve the special relativistic hydrodynamics equations on Cartesian grids. We then blend the scheme with a first-order finite volume scheme to control the oscillations near discontinuities. We also use a scaling limiter to preserve the physical admissibility of the solution after ensuring the scheme is admissible in means. A particular focus is given to designing a discontinuity indicator model to detect the local non-smoothness in the solution of the highly non-linear relativistic hydrodynamics equations. Finally, we present numerical results for a wide range of test cases to show the robustness and efficiency of the proposed scheme. |
| title | Bound Preserving Lax-Wendroff Flux Reconstruction Method for Special Relativistic Hydrodynamics |
| topic | Numerical Analysis 65M60 G.1.8 |
| url | https://arxiv.org/abs/2409.15805 |