A positivity-preserving adaptive-order finite-difference scheme for GRMHD
Creators
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1.
Cornell University
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2.
California Institute of Technology
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3.
California State University, Fullerton
Abstract
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 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.
Copyright and License
© 2023 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.
Acknowledgement
We are grateful to Michael Pajkos for feedback and informative discussions on the paper, especially the visualizations. SpECTRE uses Charm++/Converse [77, 78], which was developed by the Parallel Programming Laboratory in the Department of Computer Science at the University of Illinois at Urbana-Champaign. SpECTRE uses Blaze [79, 80], HDF5 [81], the GNU Scientific Library (GSL) [82], yaml-cpp [83], pybind11 [84], libsharp [85], and LIBXSMM [86]. The figures in this article were produced with matplotlib [87, 88], NumPy [89], and ParaView [90, 91]. Computations were performed with the Wheeler cluster at Caltech.
Funding
This work was supported in part by the Sherman Fairchild Foundation and by NSF Grants PHY-2011961, PHY-2011968, and OAC-2209655 at Caltech, and NSF Grants PHY-2207342 and OAC-2209655 at Cornell. This work was supported in part by NSF Grants PHY-1654359 and PHY-2208014, by the Dan Black Family Trust, and by Nicholas and Lee Begovich.
Data Availability
The data that support the findings of this study are openly available at the following URL/DOI: https://github.com/sxs-collaboration/spectre/ [49].
Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2306.04755 (arXiv)
- Is supplemented by
- Dataset: https://github.com/sxs-collaboration/spectre/ (URL)
Funding
- Sherman Fairchild Foundation
- National Science Foundation
- PHY-2011961
- National Science Foundation
- PHY-2011968
- National Science Foundation
- OAC-2209655
- National Science Foundation
- PHY-2207342
- National Science Foundation
- PHY-1654359
- National Science Foundation
- PHY-2208014
- Dan Black Family Trust
- Nicholas and Lee Begovich
Dates
- Accepted
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2023-11-01
- Available
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2023-11-21Published online