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

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

2003-10-28

arxiv.org/abs/astro-ph/0310790v1

Mon.Not.Roy.Astron.Soc. 348 (2004) 139

Astronomy and Astrophysics

Astrophysics

14 pages, 4 figures, accepted to MNRAS

Scientific paper

10.1111/j.1365-2966.2004.07346.x

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 (Price and Monaghan 2003a, paper I) for non ideal MHD where artificial dissipative terms were included to handle shocks.

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