Simulating anisotropic thermal conduction in supernova remnants - I. Numerical methods

Anisotropic thermal conduction plays an important role in various astrophysical systems. One of the most stringent tests of thermal conduction can be found in supernova remnants. In this paper we study anisotropic thermal conduction and examine the physical nature of the flux of thermal conduction in the classical and saturated limits. We also present a temporally second-order accurate implicit-explicit scheme for the time-update of thermal conduction terms within a numerical magnetohydrodynamics (MHD) scheme. Several useful tests are presented showing that the method works well. We also present a convergence study of the hot gas produced in thermally conducting, magnetized supernova remnants and show that the resolutions used here provide reasonably accurate results.