A High Order Godunov Scheme with Constrained Transport and Adaptive Mesh Refinement for Astrophysical MHD

摘要

In this paper, we present a new method to perform numerical simulations ofastrophysical MHD flows using the Adaptive Mesh Refinement framework andConstrained Transport. The algorithm is based on a previous work in which theMUSCL--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 discussits properties. Through a series of test problems, we illustrate theperformances of this new code using two different MHD Riemann solvers(Lax-Friedrich and Roe) and the need of the Adaptive Mesh Refinementcapabilities in some cases. Finally, we show its versatility by applying it totwo completely different astrophysical situations well studied in the pastyears: the growth of the magnetorotational instability in the shearing box andthe collapse of magnetized cloud cores. We have implemented this new Godunovscheme to solve the ideal MHD equations in the AMR code RAMSES. It results in apowerful tool that can be applied to a great variety of astrophysical problems,ranging from galaxies formation in the early universe to high resolutionstudies of molecular cloud collapse in our galaxy.