An explicit divergence-free DG method for incompressible magnetohydrodynamics
Abstract
We extend the recently introduced explicit divergence-free DG scheme for incompressible hydrodynamics [arXiv:1808.04669]. to the incompressible magnetohydrodynamics (MHD). A globally divergence-free finite element space is used for both the velocity and the magnetic field. Highlights of the scheme includes global and local conservation properties, high-order accuracy, energy-stability, pressure-robustness. When forward Euler time stepping is used, we need two symmetric positive definite (SPD) hybrid-mixed Poisson solvers (one for velocity and one for magnetic field) to advance the solution to the next time level. Since we treat both viscosity in the momentum equation and resistivity in the magnetic induction equation explicitly, the method shall be best suited for inviscid or high-Reynolds number, low resistivity flows so that the CFL constraint is not too restrictive.
Keywords
Cite
@article{arxiv.1808.08119,
title = {An explicit divergence-free DG method for incompressible magnetohydrodynamics},
author = {Guosheng Fu},
journal= {arXiv preprint arXiv:1808.08119},
year = {2018}
}
Comments
14 pages, 8 figures. arXiv admin note: text overlap with arXiv:1808.04669