A positivity-preserving adaptive-order finite-difference scheme for GRMHD
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916095744540672 |
|---|---|
| author | Deppe, Nils Kidder, Lawrence E. Teukolsky, Saul A. Bonilla, Marceline S. Hébert, François Kim, Yoonsoo Scheel, Mark A. Throwe, William Vu, Nils L. |
| author_facet | Deppe, Nils Kidder, Lawrence E. Teukolsky, Saul A. Bonilla, Marceline S. Hébert, François Kim, Yoonsoo Scheel, Mark A. Throwe, William Vu, Nils L. |
| contents | We present an adaptive-order positivity-preserving conservative finite-difference scheme that allows a high-order solution away from shocks and discontinuities while guaranteeing positivity and robustness at discontinuities. This is achieved by monitoring the relative power in the highest mode of the reconstructed polynomial and reducing the order when the polynomial series no longer converges. Our approach is similar to the multidimensional optimal order detection (MOOD) strategy, but differs in several ways. The approach is a priori and so does not require retaking a time step. It can also readily be combined with positivity-preserving flux limiters that have gained significant traction in computational astrophysics and numerical relativity. This combination ultimately guarantees a physical solution both during reconstruction and time stepping. We demonstrate the capabilities of the method using a standard suite of very challenging 1d, 2d, and 3d general relativistic magnetohydrodynamics test problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_04755 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A positivity-preserving adaptive-order finite-difference scheme for GRMHD Deppe, Nils Kidder, Lawrence E. Teukolsky, Saul A. Bonilla, Marceline S. Hébert, François Kim, Yoonsoo Scheel, Mark A. Throwe, William Vu, Nils L. High Energy Astrophysical Phenomena General Relativity and Quantum Cosmology We present an adaptive-order positivity-preserving conservative finite-difference scheme that allows a high-order solution away from shocks and discontinuities while guaranteeing positivity and robustness at discontinuities. This is achieved by monitoring the relative power in the highest mode of the reconstructed polynomial and reducing the order when the polynomial series no longer converges. Our approach is similar to the multidimensional optimal order detection (MOOD) strategy, but differs in several ways. The approach is a priori and so does not require retaking a time step. It can also readily be combined with positivity-preserving flux limiters that have gained significant traction in computational astrophysics and numerical relativity. This combination ultimately guarantees a physical solution both during reconstruction and time stepping. We demonstrate the capabilities of the method using a standard suite of very challenging 1d, 2d, and 3d general relativistic magnetohydrodynamics test problems. |
| title | A positivity-preserving adaptive-order finite-difference scheme for GRMHD |
| topic | High Energy Astrophysical Phenomena General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2306.04755 |