WENO-WOMBAT: Scalable Fifth-order Constrained-transport Magnetohydrodynamics for Astrophysical Applications

Owing to increases in computing power, high-order Eulerian schemes will likely become instrumental in simulations of turbulence and magnetic field amplification in astrophysical fluids in the next years. We present the implementation of a fifth-order weighted essentially non-oscillatory scheme for constrained-transport magnetohydrodynamics in the code WOMBAT. We establish the correctness of our implementation with extensive number tests. We find that the fifth-order scheme performs as accurately as a common second-order scheme at half the resolution. We argue that for a given solution quality, the new scheme is more computationally efficient than lower order schemes in three dimensions. We also establish the performance characteristics of the solver in the WOMBAT framework. Our implementation fully vectorizes using flattened arrays in thread-local memory. It performs at about 0.6 million zones per second per node on Intel Broadwell. We present scaling tests of the code on up to 98,000 cores on the Cray XC40 machine "Hazel Hen," with a sustained performance of about 5% of peak at scale.