An Explicit Scheme for Incorporating Ambipolar Diffusion in a Magnetohydrodynamics Code

TL;DR

This paper presents a second-order accurate, explicit numerical scheme for incorporating ambipolar diffusion into multidimensional magnetohydrodynamics simulations, ensuring divergence-free magnetic fields and accelerating computations with super time stepping.

Contribution

The authors develop a fully unsplit, explicit finite difference method with flux-interpolated constrained transport for ambipolar diffusion in MHD codes, validated by multiple tests.

Findings

The scheme accurately models oblique C-type shocks and Alfvén wave decay.

Simulations reveal ambipolar diffusion significantly influences MHD turbulence dissipation.

The method effectively handles complex MHD flows with ambipolar diffusion.

Abstract

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 Alfv\'en 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.