An HLLC Riemann solver for relativistic flows – II. Magnetohydrodynamics

By Andrea Mignone, Gianluigi Bodo. 2006

149 citations recorded by the source corpus.

An approximate Riemann solver for the equations of relativistic magnetohydrodynamics (RMHD) is derived. The Harten–Lax–van Leer contact wave (HLLC) solver, originally developed by Toro, Spruce and Spears, generalizes the algorithm described in a previous paper to the case where magnetic fields are present. The solution to the Riemann problem is approximated by two constant states bounded by two fast shocks and separated by a tangential wave. The scheme is Jacobian-free, in the sense that it avoids the expensive characteristic decomposition of the RMHD equations and it improves over the HLL scheme by restoring the missing contact wave. Multidimensional integration proceeds via the single step, corner transport upwind (CTU) method of Colella, combined with the constrained transport (CT) algorithm to preserve divergence-free magnetic fields. The resulting numerical scheme is simple to implement, efficient and suitable for a general equation of state. The robustness of the new algorithm is validated against one- and two-dimensional numerical test problems.

Subfields: Astronomy and Astrophysics, Computational Mechanics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/87b4f2963337892b807dd1250bd46d1a3f7c3209

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Citations in the corpus

PLUTO: A Numerical Code for Computational Astrophysics (2007, methodology): “The RMHD module may be used with the Lax-Friedrichs, HLL, or the recently developed HLLC Riemann solver; see Mignone & Bodo (2006).”
ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics (2007, methodology): “In order to pass it with the original settings, ad hoc numerical strategies could be introduced, such as adding artificial viscosity and/or resistivity (Komissarov 1999) or resetting the energy and reducing to first order in critical situations (Mignone & Bodo 2006).”
Beyond ideal MHD: towards a more realistic modelling of relativistic astrophysical plasmas (2008, background): “…Koldoba et al. 2002; Gammie et al. 2003; Del Zanna et al. 2003; Anninos et al. 2005; Duez et al. 2005; Shibata & Sekiguchi 2005; Neilsen et al. 2006; Anton et al. 2006; McKinney 2006a; Mignone & Bodo 2006; Noble et al. 2007; Giacomazzo & Rezzolla 2007; Del Zanna et al. 2007; Farris et al. 2008).”
The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers (2020, methodology): “…(Teyssier 2002; Lamberts et al. 2012) uses a modified enthalpy-based method from Mignone & McKinney (2007), PLUTO (Mignone et al. 2007; Mignone 2014) uses the enthalpy-based 1D method of Mignone & Bodo (2006), and BHAC uses both an enthalpy-based 1D method and a 2D method (Porth et al. 2017).”