Speaker: Prateek Sharma, Graduate Student, Astrophysics, Princeton
Various finite difference methods used for numerical implementation of anisotropic thermal conduction along the magnetic field direction will be discussed. The simplest methods based on centered differencing (symmetric and asymmetric methods) are discussed in Gunter et al. JCP, v. 209, p. 354, 2005. These can give rise to heat flowing from lower to higher temperatures in presence of large temperature gradients, causing the temperature to become negative at some places! Simple numerical tests will be presented to demonstrate this fact. I will discuss why heat can flow in the `wrong' direction. Implementation of anisotropic conduction based on slope limiters (analogous to those used in hyperbolic equations, e.g., minmod, monotonized central etc.) will be presented. Heat fluxes based on `limited' temperature gradients do not amplify temperature extrema and are suitable for cases with large temperature gradients. Large temperature gradients occur in many astrophysical plasmas, e.g., disk-corona boundary, collisionless shocks, and transition regions between hot and warm phases of interstellar medium.