Magnetohydrodynamics with GAMER

GAMER, a parallel Graphic-processing-unit-accelerated Adaptive-MEsh-Refinement hydrodynamic code, has been extended to support magnetohydrodynamics (MHD) with both the corner-transport-upwind (CTU) and MUSCL-Hancock schemes and the constraint transport (CT) technique. The divergent preserving operator for adaptive mesh refinement (AMR) has been applied to reinforce the divergence-free constraint on the magnetic field. GAMER-MHD has fully exploited the concurrent executions between the GPU MHD solver and other CPU computation pertinent to AMR. We perform various standard tests to demonstrate that GAMER-MHD is both second-order accurate and robust, producing results as accurate as those given by high-resolution uniform-grid runs. We also explore a new 3D MHD test, where the magnetic field assumes the Arnold-Beltrami-Childress (ABC) configuration, temporarily becomes turbulent with current sheets and finally settles to a lowest-energy equilibrium state. This 3D problem is adopted for the performance test of GAMER-MHD. The single-GPU performance reaches $1.2\times 10^8$ and $5.5\times 10^7$ cell-updates/sec for the single- and double-precision calculations, respectively, on Tesla P100. We also demonstrate a parallel efficiency of $\sim 70\%$ for both weak and strong scaling using $1,024$ XK nodes on the Blue Waters supercomputers.