A Gradient Recovery Method for Electron Magnetohydrodynamics with Fractional Dissipation
It provides a stable and accurate numerical scheme for simulating electron magnetohydrodynamics with fractional dissipation, which is relevant for plasma physics applications.
The paper proposes a structure-preserving numerical method for the 2.5D electron magnetohydrodynamics system with fractional dissipation, achieving second-order spatial convergence and stable Hall-driven dynamics in benchmark tests.
We propose and analyze a structure-preserving numerical method for the $2\tfrac{1}{2}$-dimensional (2.5D) electron magnetohydrodynamics system with fractional dissipation on the periodic torus. The method works directly with the magnetic field components and combines this component formulation with the gradient recovery operator of [T. Chu, H. Guo, and Z. Zhang, SIAM J. Numer. Anal., 63 (2025), pp. 23--53]. We establish discrete energy stability for a semi-implicit structure-preserving formulation and use an explicit-Hall integrating-factor implementation for efficient computation on periodic grids. The fractional dissipation is treated exactly in Fourier space, and the in-plane divergence constraint is enforced by a spectral Hodge projection. Numerical experiments demonstrate second-order spatial convergence and stable Hall-driven dynamics across several benchmark tests.