High-Order Numerical Methods for Magnetohydrodynamic Turbulence

Magnetized turbulence is ubiquitous throughout astrophysical and terrestrial plasmas, and yet our understanding of its most basic form, ideal magnetohydrodynamic (MHD) turbulence, remains far from complete. Previous studies have explored energy transfer within and between kinetic and magnetic reservoirs, but numerical dissipation has hindered a full understanding of the energy cascade. In this work, we introduce Spartha, a high-order, weighted essentially non-oscillatory code to model ideal MHD turbulence. We examine how increasing the order of numerical methods influences the energy cascade. Specifically, we show that higher-order methods reduce spatial resolution requirements, extend the inertial range, and mitigate numerical dissipation, thereby improving our understanding of the energy cascade.