Smoothed particle magnetohydrodynamics with a Riemann solver and the method of characteristics

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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.