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Journal Article

Robust Recovery of Primitive Variables in Relativistic Ideal Magnetohydrodynamics


Kastaun,  Wolfgang
Binary Merger Observations and Numerical Relativity, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;

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Kastaun, W., Kalinani, J. V., & Ciolfi, R. (2021). Robust Recovery of Primitive Variables in Relativistic Ideal Magnetohydrodynamics. Physical Review D, 103: 023018. doi:10.1103/PhysRevD.103.023018.

Cite as: https://hdl.handle.net/21.11116/0000-0007-F878-B
Modern simulation codes for general relativistic ideal magnetohydrodynamics
are all facing a long standing technical problem given by the need to recover
fundamental variables from those variables that are evolved in time. In the
relativistic case, this requires the numerical solution of a system of
nonlinear equations. Although several approaches are available, none has proven
completely reliable. A recent study comparing different methods showed that all
can fail, in particular for the important case of strong magnetization and
moderate Lorentz factors. Here, we propose a new robust, efficient, and
accurate solution scheme, along with a proof for the existence and uniqueness
of a solution, and analytic bounds for the accuracy. Further, the scheme allows
us to reliably detect evolution errors leading to unphysical states and
automatically applies corrections for typical harmless cases. A reference
implementation of the method is made publicly available as a software library.
The aim of this library is to improve the reliability of binary neutron star
merger simulations, in particular in the investigation of jet formation and
magnetically driven winds.