Smoothed particle magnetohydrodynamics with the geometric density average force expression

We present a novel method of magnetohydrodynamics (MHD) within the smoothed particle hydrodynamics scheme using the Geometric Density average force expression (GDSPH). GDSPH has recently been shown to reduce the leading order errors and greatly improve the accuracy near density discontinuities, eliminating surface tension effects. Here, we extend the study to investigate how SPMHD benefits from this method. We implement ideal MHD in the Gasoline2 and Changa codes with both GDSPH and traditional SPH (TSPH) schemes. An constrained hyperbolic divergence cleaning scheme is employed to control the divergence error, and a switch for artificial resistivity with minimized dissipation is used. We test the codes with a large suite of MHD tests, and show that in all problems the results are comparable or improved over previous SPMHD implementations. While both GDSPH and TSPH perform well with relatively smooth or highly supersonic flows, GDSPH shows significant improvements in the presence of strong discontinuities and large dynamic scales. In particular, when applied to an astrophysical problem of the collapse of a magnetized cloud, GDSPH realistically captures the development of a magnetic tower and jet launching in the weak-field regime, and exhibit fast convergence with resolution, while TSPH failed to do so. Our new method shows qualitatively similar results to the ones from the meshless finite mass/volume (MFM/MFV) schemes within the Gizmo code, while remaining computationally less expensive.