Two-dimensional MHD smoothed particle hydrodynamics stability analysis

Smoothed particle hydrodynamics (SPH) is an N-body integration scheme widely used within the field of astrophysics. Unfortunately, the method has up until recently been facing serious problems concerning instabilities when applied to MHD problems. Regularized smoothed particle hydrodynamics (RSPH) was proposed as an extension to SPH with the aim of achieving high-accuracy modeling of hydrodynamic and magnetohydrodynamic problems. This work included a new formulation of the discrete MHD equations that is easily implemented into SPH and RSPH codes alike. In this paper, the stability properties of two-dimensional linear MHD waves using this formulation are investigated. The presented analysis shows that linear stability properties similar to that obtained for sound waves in the absence of a magnetic field is achieved also for MHD waves. This result is confirmed by the included test results using both standard SPH and RSPH.