Project Description

This project aims to develop a robust, GPU-accelerated high-order Spectral Difference solver for the Hall magnetohydrodynamics (MHD) equations to enable predictive simulations of magnetic reconnection in weakly collisional plasmas. Magnetic reconnection plays a central role in rapid energy release in both space and laboratory plasmas, yet standard resistive MHD models fail to reproduce key experimentally observed features such as fast reconnection rates, thin current sheets, and Hall-induced magnetic structures. Building on our recently validated Spectral Difference with Divergence Cleaning (SDDC) framework and the comparative Hall-versus-MHD reconnection study of Hankey et al. (2023), this work will incorporate Hall physics, improved Bassi–Rebay II viscous fluxes for enhanced stability, and GPU acceleration to overcome the severe stiffness and computational cost associated with Hall MHD. The resulting solver will resolve Hall-scale dispersive effects, whistler dynamics, and magnetic island formation with substantially higher accuracy than low-order approaches. Using high-resolution two-dimensional reconnection benchmarks on meshes significantly finer than previous studies, we will quantify differences between Hall MHD and standard MHD in reconnection rate, current-sheet evolution, and magnetic topology, with direct relevance to both heliophysical and laboratory plasma environments. Through open-source dissemination and integration into undergraduate education, this project will advance state-of-the-art computational plasma modeling while training students in high-performance scientific computing and plasma physics.