Incorporating Ambipolar and Ohmic Diffusion in the AMR MHD code RAMSES

TL;DR

This paper presents the implementation of ambipolar and Ohmic diffusion effects in the RAMSES MHD code, enabling more accurate simulations of star formation and molecular cloud dynamics with non-ideal MHD physics.

Contribution

The authors developed and validated a second-order accurate scheme for non-ideal MHD effects in the RAMSES code, including detailed discretization and stability analysis.

Findings

Scheme is second-order accurate.

Numerical diffusion characterized and controlled.

Suitable for star formation and molecular cloud studies.

Abstract

We have implemented non-ideal Magneto-Hydrodynamics (MHD) effects in the Adaptive Mesh Refinement (AMR) code RAMSES, namely ambipolar diffusion and Ohmic dissipation, as additional source terms in the ideal MHD equations. We describe in details how we have discretized these terms using the adaptive Cartesian mesh, and how the time step is diminished with respect to the ideal case, in order to perform a stable time integration. We have performed a large suite of test runs, featuring the Barenblatt diffusion test, the Ohmic diffusion test, the C-shock test and the Alfven wave test. For the latter, we have performed a careful truncation error analysis to estimate the magnitude of the numerical diffusion induced by our Godunov scheme, allowing us to estimate the spatial resolution that is required to address non-ideal MHD effects reliably. We show that our scheme is second-order accurate, and is therefore ideally suited to study non-ideal MHD effects in the context of star formation and molecular cloud dynamics.