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

There have been some issues in the past in attempts to simulate magnetic fields using the Smoothed Particle Hydrodynamics (SPH) method. SPH is well suited to star formation problems because of its Lagrangian nature. We present new, stable and conservative methods for magnetohydrodynamics (MHD) in SPH and present numerical tests in one dimension to show that it gives robust and accurate results.