Systematic Comparison between Constrained Transport and Mixed Divergence Cleaning Methods for Astrophysical Magnetohydrodynamic Simulations
Kengo Tomida, Kenji Eric Sadanari, Shinsuke Takasao, Kazunari Iwasaki
TLDR
This paper systematically compares Constrained Transport (CT) and Dedner's divergence cleaning for MHD simulations, finding CT more accurate.
Key contributions
- Systematically compares Constrained Transport (CT) and Dedner's mixed divergence cleaning in MHD simulations.
- Finds Dedner's scheme creates artifacts with localized magnetic fields or sudden timestep changes.
- Suggests previous astrophysical findings, like rapid magnetic field growth, may be inaccurate.
- Proposes modifications for divergence cleaning, but concludes CT is more accurate and reliable.
Why it matters
This paper highlights critical issues in widely used MHD simulation methods, showing how divergence cleaning can produce significant artifacts. It suggests that some previous astrophysical findings might need re-evaluation and provides insights for more reliable future simulations, ensuring greater accuracy in modeling cosmic phenomena.
Original Abstract
Magnetohydrodynamic (MHD) simulations are indispensable research infrastructure in astrophysics today. In order to satisfy the solenoidal constraint of the MHD equations on discretized grids, modern simulation codes often employ either constrained transport (CT) with a staggered grid or divergence cleaning using an additional variable. We compare CT and Dedner's mixed divergence cleaning schemes systematically, and find that the divergence cleaning scheme can produce substantial artifacts in certain situations. Through numerical experiments including both idealized tests and practical applications, we show that the original implementation of Dedner's scheme becomes inaccurate when magnetic fields are strongly localized or when the timestep suddenly changes. We find that some previous results, such as the extremely rapid growth of magnetic fields during star formation in the early Universe, may be affected by the spurious behavior of the divergence cleaning scheme. We propose a few modifications to improve the robustness of the divergence cleaning method. Nevertheless, we find that the CT scheme is more accurate and reliable in many situations.
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