An Explicit Scheme for Incorporating Ambipolar Diffusion in a Magnetohydrodynamics Code

We describe a method for incorporating ambipolar diffusion in the strong coupling approximation into a multidimensional magnetohydrodynamics code based on the total variation diminishing scheme. Contributions from ambipolar diffusion terms are included by explicit finite difference operators in a fully unsplit way, maintaining second order accuracy. The divergence-free condition of magnetic fields is exactly ensured at all times by a flux-interpolated constrained transport scheme. The super time stepping method is used to accelerate the timestep in high resolution calculations and/or in strong ambipolar diffusion. We perform two test problems, the steady-state oblique C-type shocks and the decay of Alfvén waves, confirming the accuracy and robustness of our numerical approach. Results from the simulations of the compressible MHD turbulence with ambipolar diffusion show the flexibility of our method as well as its ability to follow complex MHD flows in the presence of ambipolar diffusion. These simulations show that the dissipation rate of MHD turbulence is strongly affected by the strength of ambipolar diffusion. Subject headings: diffusion — ISM: clouds — methods: numerical — MHD — stars: formation — turbulence International Center for Astrophysics, Korea Astronomy and Space Science Institute, Daejeon 305-348, Korea; [email protected], [email protected]. Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK. Department of Physics and Astronomy, Georgia State University, P.O. Box 4106, Atlanta, GA 303024106; [email protected]. School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540.