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 non-linear Riemann problem with magnetic pressure for compressive waves and apply the method of characteristics for Alfven 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.