SPMHD with the geometric density force gradient operator

Magnetic fields are an essential part to a wide array of different astrophysical systems. While Eulerian codes with robust magnetohydrodynamic (MHD) algorithms have existed for a long time, Lagrangian codes with comparable sophistication have only more recently been developed. The benefit of Lagrangian codes comes when modeling system's which are highly dynamic and have a wide range of spatial scales, such as galaxy formation. Smoothed particle hydrodynamics (SPH) is a popular meshless Lagrangian method, which have seen tremendous improvements in recent years. One major issue which have been tackled is the numerical surface tension effect, which effectively inhibited mixing in SPH. This issue was shown to be resolved with the use of a geometric density weighting on the force calculation (GDSPH). During this talk, we will investigate if SPMHD could also benefit from the GDSPH formulation. We will show that while many of the standard tests show similar results to traditional SPMHD, significant improvements are seen in the case of jet launching and the magneto rotational instability,  showing comparable results to the MFM/MFV methods which employ more complex gradient estimates and fluxes from Riemann solvers.