# WENO-Wombat: Scalable Fifth-Order Constrained-Transport Magnetohydrodynamics for Astrophysical Applications

## TL;DR

This paper introduces a fifth-order weighted essentially non-oscillatory scheme for constrained-transport magnetohydrodynamics in the WOMBAT code, demonstrating improved accuracy and efficiency for astrophysical fluid simulations.

## Contribution

The paper presents the implementation and validation of a novel fifth-order scheme in WOMBAT, enhancing accuracy and computational efficiency for astrophysical MHD simulations.

## Key findings

- Fifth order scheme matches second order accuracy at half the resolution.
- The scheme is more computationally efficient than lower order schemes in 3D.
- The implementation scales well on high-performance computing systems.

## Abstract

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.