Smoothed particle magnetohydrodynamics with a Riemann solver and the   method of characteristics
  In this paper, we develop a new method for magnetohydrodynamics (MHD) using smoothed particle hydrodynamics (SPH). To describe MHD shocks accurately, the Godunov method is applied to SPH instead of artificial dissipation terms. In the interaction between particles, we solve a nonlinear Riemann problem with magnetic pressure for compressive waves and apply the method of characteristics for Alfv{\'e}n waves. An extensive series of MHD test calculations is performed. In all test calculations, we compare the results of our SPH code with those of a finite-volume method with an approximate Riemann solver, and confirm excellent agreement. 
Kazunari Iwasaki and Shu-ichiro Inutsuka
astro-ph.GA astro-ph.IM