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Title:
Smoothed Particle Magnetohydrodynamics - II. Variational principles and variable smoothing-length terms
Authors:
Price, D. J.; Monaghan, J. J.
Affiliation:
AA(Institute of Astronomy, Madingley Road, Cambridge CB3 0HA), AB(School of Mathematical Sciences, Monash University, Clayton 3800, Australia)
Publication:
Monthly Notices of the Royal Astronomical Society, Volume 348, Issue 1, pp. 139-152. (MNRAS Homepage)
Publication Date:
02/2004
Origin:
MNRAS
MNRAS Keywords:
magnetic fields, MHD, methods: numerical
DOI:
10.1111/j.1365-2966.2004.07346.x
Bibliographic Code:
2004MNRAS.348..139P

Abstract

In this paper we show how a Lagrangian variational principle can be used to derive the Smoothed Particle Magnetohydrodynamics (SPMHD) equations for ideal Magnetohydrodynamics (MHD). We also consider the effect of a variable smoothing length in the Smoothed Particle Hydrodynamics (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 the companion paper for non-ideal MHD where artificial dissipative terms were included to handle shocks.

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