Open AccessSmoothed Particle Magnetohydrodynamics – I. Algorithm and tests in one dimension
Author(s) -
Price D. J.,
Monaghan J. J.
Publication year - 2004
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1111/j.1365-2966.2004.07345.x
Subject(s) - magnetohydrodynamics , physics , smoothed particle hydrodynamics , adiabatic process , dissipation , dimension (graph theory) , classical mechanics , statistical physics , magnetic field , algorithm , mechanics , computer science , mathematics , quantum mechanics , pure mathematics
In this paper we show how the Smoothed Particle Hydrodynamics (SPH) equations for ideal Magnetohydrodynamics (MHD) can be written in conservation form with the positivity of the dissipation guaranteed. We call the resulting algorithm Smoothed Particle Magnetohydrodynamics (SPMHD). The equations appear to be accurate, robust and easy to apply and do not suffer from the instabilities known to exist previously in formulations of the SPMHD equations. In addition we formulate our MHD equations such that errors associated with non‐zero divergence of the magnetic field are naturally propagated by the flow and should therefore remain small. In this and the companion paper we present a wide range of numerical tests in one dimension to show that the algorithm gives very good results for one‐dimensional flows in both adiabatic and isothermal MHD. For the one‐dimensional tests the field structure is either two‐ or three‐dimensional. The algorithm has many astrophysical applications and is particularly suited to star‐formation problems.