An Implicit Scheme for Ohmic Dissipation with Adaptive Mesh Refinement

TL;DR

This paper introduces an implicit Crank-Nicolson based method for simulating ohmic dissipation in magnetized plasmas, integrated into an adaptive mesh refinement code, reducing computational costs while maintaining accuracy.

Contribution

It presents a novel implicit scheme for ohmic dissipation that is compatible with AMR and demonstrates efficient convergence and accuracy in test problems.

Findings

The method achieves second-order accuracy in time and space.

It converges rapidly on AMR grids, depending on parameters.

It reduces computational costs compared to explicit methods.

Abstract

An implicit method for the ohmic dissipation is proposed. The proposed method is based on the Crank-Nicolson method and exhibits second-order accuracy in time and space. The proposed method has been implemented in the SFUMATO adaptive mesh refinement (AMR) code. The multigrid method on the grids of the AMR hierarchy converges the solution. The convergence is fast but depends on the time step, resolution, and resistivity. Test problems demonstrated that decent solutions are obtained even at the interface between fine and coarse grids. Moreover, the solution obtained by the proposed method shows good agreement with that obtained by the explicit method, which required many time steps. The present method reduces the number of time steps, and hence the computational costs, as compared with the explicit method.