Gradient particle magnetohydrodynamics: A Lagrangian particle code for astrophysical magnetohydrodynamics

We introduce a new algorithm, gradient particle magnetohydrodynamics (GPM), for the numerical simulation of astrophysical MHD phenomena. The GPM prescription employs a local polynomial fit to recover accurate gradient information from a disordered distribution of particles. This Lagrangian particle method evolves the vector potential to eliminate the problem of magnetic divergence. Validation tests of MHD waves, an advection problem, and an MHD Riemann problem are presented to demonstrate the viability of GPM as a new tool for the investigation of MHD problems in astrophysics.