Gradient Particle Magnetohydrodynamics (GPM) is introduced as a new Lagrangian particle method for astrophysical MHD simulation. Convergence, stability, and maintenance of zero magnetic divergence is discussed. The results of validation test problems are presented. Lagrangian methods must confront not only the standard truncation error, but also a characteristic error in sampling of the local environment, dubbed disconnection error. To reduce truncation error, a generally adaptive scheme for Lagrangian methods has been developed, Adaptive Particle Refinement (APR). The APR strategy is outlined and promising preliminary results are presented. Finally, the disconnection error and a related computational instability are described. Control of the disconnection error can be achieved by ensuring nearest neighbors are mutual neighbors.
Copyright. All Rights Reserved.