Astrophysical weighted particle magnetohydrodynamics

This paper presents applications of a weighted meshless scheme for conservation laws to the Euler equations and the equations of ideal magnetohydrodynamics (MHD). The divergence constraint of the latter is maintained to the truncation error by a new meshless divergence cleaning procedure. The physics of the interaction between the particles is described by a one-dimensional Riemann problem in a moving frame. As a result, the necessary diffusion which is required to treat dissipative processes is added automatically. Our scheme therefore has no free parameters that control the physics of interparticle interaction, with the exception of the number of interacting neighbours which control the resolution and accuracy. The resulting equations have a form similar to smoothed particle hydrodynamics (SPH) equations, and therefore existing SPH codes can be used to implement the weighed particle scheme. The scheme is validated in several hydrodynamic and MHD test cases. In particular, we demonstrate for the first time the ability of a meshless MHD scheme to model magnetorotational instability in accretion discs.