An implicit scheme for solving the anisotropic diffusion of heat and cosmic rays in the RAMSES code

¹ Institut d’Astrophysique de Paris, UMR 7095, CNRS, UPMC Univ. Paris VI, 98bis boulevard Arago, 75014 Paris, France
e-mail: dubois@iap.fr
² École Normale Supérieure de Lyon, CRAL, UMR 5574 du CNRS, Université de Lyon I, 46 allée d’Italie, 69364 Lyon Cedex 07, France
e-mail: benoit.commercon@ens-lyon.fr

Received: 5 August 2015
Accepted: 31 October 2015

Abstract

Astrophysical plasmas are subject to a tight connection between magnetic fields and the diffusion of particles, which leads to an anisotropic transport of energy. Under the fluid assumption, this effect can be reduced to an advection-diffusion equation, thereby augmenting the equations of magnetohydrodynamics. We introduce a new method for solving the anisotropic diffusion equation using an implicit finite-volume method with adaptive mesh refinement and adaptive time-stepping in the ramses code. We apply this numerical solver to the diffusion of cosmic ray energy and diffusion of heat carried by electrons, which couple to the ion temperature. We test this new implementation against several numerical experiments and apply it to a simple supernova explosion with a uniform magnetic field.