  Due to increase in computing power, high-order Eulerian schemes will likely
become instrumental for the 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 into the code WOMBAT. We establish
the correctness of our implementation with an 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 up to
98 thousand cores on the Cray XC40 machine "Hazel Hen", with a sustained
performance of about 5 percent of peak at scale.
