A semi-implicit Hall-MHD solver using whistler wave preconditioning

TL;DR

This paper introduces a semi-implicit Hall-MHD solver that effectively handles whistler wave dispersive effects, allowing larger time steps and improved stability in simulations of magnetic reconnection.

Contribution

A novel semi-implicit scheme with whistler wave preconditioning is developed, enabling efficient and stable numerical integration of Hall-MHD equations with potential multigrid acceleration.

Findings

The scheme achieves stable integration with larger time steps.

Short wavelengths converge faster, aiding multigrid methods.

Applied successfully to a magnetic reconnection problem.

Abstract

The dispersive character of the Hall-MHD solutions, in particular the whistler waves, is a strong restriction to numerical treatments of this system. Numerical stability demands a time step dependence of the form $\Delta t\propto (\Delta x)^2$ for explicit calculations. A new semi--implicit scheme for integrating the induction equation is proposed and applied to a reconnection problem. It it based on a fix point iteration with a physically motivated preconditioning. Due to its convergence properties, short wavelengths converge faster than long ones, thus it can be used as a smoother in a nonlinear multigrid method.