Smoothed Particle Magnetohydrodynamics II. Variational principles and variable smoothing length terms

D.J. Price, J.J. Monaghan

Institute of Astronomy, Madingley Rd, Cambridge, CB3 0HA, UK
School of Mathematical Sciences, Monash University, Clayton 3800, Australia

Submitted: 6th June 2003; Accepted: 28th October 2003

NB: a more up-to-date version of this work may be found in my PhD thesis
[ Paper I ][ Paper II ][ PhD Thesis ][ Paper III ][ Paper IV ]


In this paper we show how a Lagrangian variational principle can be used to derive the SPMHD (Smoothed Particle Magnetohydrodynamics) equations for ideal MHD. We also consider the effect of a variable smoothing length in the SPH kernels after which we demonstrate by numerical tests that the consistent treatment of terms relating to the gradient of the smoothing length in the SPMHD equations significantly improves the accuracy of the algorithm. Our results complement those obtained in a companion paper (\citealt{pm03a}, paper I) for non ideal MHD where artificial dissipative terms were included to handle shocks.

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