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

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

2007-12-15

arxiv.org/abs/0712.2506v1

Physics

Computational Physics

Scientific paper

10.1016/j.cpc.2007.11.018

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.

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