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

TL;DR

This paper introduces a novel smoothed particle magnetohydrodynamics method that employs a Riemann solver and characteristics to accurately model MHD shocks, showing excellent agreement with traditional finite-volume methods.

Contribution

It develops a new SPH-based MHD approach using Riemann solvers and characteristics, improving shock modeling accuracy over artificial dissipation methods.

Findings

Excellent agreement with finite-volume methods in tests

Accurate modeling of MHD shocks using the new approach

Effective handling of Alfvén and compressive waves

Abstract

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.