A numerical study of magnetic reconnection: a central scheme for Hall MHD

Abstract

Over the past few years, several non-oscillatory central schemes for hyperbolic conservation laws have been proposed for approximating the solution of the Ideal MHD equations and similar astrophysical models. The simplicity, versatility, and robustness of these black-box type schemes for simulating MHD flows suggest their further development for solving MHD models with more complex wave structures. In this work we construct a non-oscillatory central scheme for the Hall MHD equations and use it to conduct a study of the magnetic reconnection phenomenon in flows governed by this model.

On Global Well-Posedness and Temporal Decay for 3D Magnetic Induction Equations with Hall Effect

“…Supposing that ρ denotes the density, u describes the velocity field of the fluid, b means the magnetic field and π is the pressure, a high-resolution, non-oscillatory, central scheme for the Hall-MHD model [1,2] can be introduced in the following:…”

“…where L 0 , δ e and δ i denotes the normalizing length limit, electron inertia and ion inertia, respectively. For the simulations considered in the work, the electron pressure tensor − δ i L 0 ∇π ρ will be ignored [2].…”

Stable finite difference schemes for the magnetic induction equation with Hall effect

“…However, the resistive MHD equations do not suffice in modeling fast magnetic reconnection. A more effective alternative is to include the Hall effect [11,15]. The resulting Ohm's law is…”

“…The Hall MHD equations are non-linear, highorder equations and are extremely complicated to study in a mathematically rigorous manner. There have been various numerical studies of the Hall MHD equations in [15,19] and references therein. However, all these papers tackle the problem from a computational point of view and do not include any rigorous results.…”