Magnetohydrodynamics with GAMER

TL;DR

GAMER-MHD is an extended GPU-accelerated adaptive mesh refinement code that accurately simulates magnetohydrodynamics, demonstrating high performance and robustness on supercomputers with standard and novel 3D tests.

Contribution

This work extends GAMER to support MHD with divergence-free constraints, GPU acceleration, and introduces a new 3D MHD test involving ABC magnetic fields.

Findings

GAMER-MHD achieves second-order accuracy and robustness.

Single-GPU performance reaches 1.2×10^8 cell-updates/sec.

Parallel efficiency of ~70% on 1024 nodes.

Abstract

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.