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

Lukas Arnold; Juergen Dreher; Rainer Grauer

doi:10.1016/j.cpc.2007.11.018

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arXiv · 0712.2506

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

Lukas Arnold·Juergen Dreher·Rainer Grauer

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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 $Δt\propto (Δx)^2$ 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.

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BibTeX RIS

Lukas Arnold, Juergen Dreher, Rainer Grauer. 2007-12-15. A semi-implicit Hall-MHD solver using whistler wave preconditioning. https://doi.org/10.1016/j.cpc.2007.11.018

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