Astronomy & Astrophysics

A&A 457, 371-384 (2006)
DOI: 10.1051/0004-6361:20065371

A high order Godunov scheme with constrained transport and adaptive mesh refinement for astrophysical magnetohydrodynamics

S. Fromang^{1, 2}, P. Hennebelle³ and R. Teyssier⁴

¹ Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
e-mail: S.Fromang@damtp.cam.ac.uk
² Astronomy Unit, Queen Mary, University of London, Mile End Road, London E1 4NS, UK
³ Laboratoire de radioastronomie millimétrique, UMR 8112 du CNRS, École normale supérieure et Observatoire de Paris, 24 rue Lhomond, 75231 Paris Cedex 05, France
⁴ Service d'Astrophysique, CEA/DSM/DAPNIA/SAp, Centre d'Études de Saclay, L'orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France

(Received 5 April 2006 / Accepted 30 June 2006 )

Abstract
Aims. In this paper, we present a new method to perform numerical simulations of astrophysical MHD flows using the Adaptive Mesh Refinement framework and Constrained Transport.
Methods. The algorithm is based on a previous work in which the MUSCL-Hancock scheme was used to evolve the induction equation. In this paper, we detail the extension of this scheme to the full MHD equations and discuss its properties.
Results. Through a series of test problems, we illustrate the performances of this new code using two different MHD Riemann solvers (Lax-Friedrich and Roe) and the need of the Adaptive Mesh Refinement capabilities in some cases. Finally, we show its versatility by applying it to two completely different astrophysical situations well studied in the past years: the growth of the magnetorotational instability in the shearing box and the collapse of magnetized cloud cores.
Conclusions. We have implemented a new Godunov scheme to solve the ideal MHD equations in the AMR code RAMSES. We have shown that it results in a powerful tool that can be applied to a great variety of astrophysical problems, ranging from galaxies formation in the early universe to high resolution studies of molecular cloud collapse in our galaxy.

Key words: magnetohydrodynamics (MHD) -- methods: numerical

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