FINMHD: An Adaptive Finite-element Code for Magnetic Reconnection and Formation of Plasmoid Chains in Magnetohydrodynamics

Abstract

Solving the problem of fast eruptive events in magnetically dominated astrophysical plasmas requires the use of particularly well adapted numerical tools. Indeed, the central mechanism based on magnetic reconnection is determined by a complex behavior with quasi-singular forming current layers enriched by their associated small scale magnetic islands called plasmoids. A new code for the solution of two dimensional dissipative magnetohydrodynamics (MHD) equations in cartesian geometry specifically developed to this end is thus presented. A current-vorticity formulation representative of an incompressible model is chosen in order to follow the formation of the current sheets and the ensuing magnetic reconnection process. A finite element discretization using triangles with quadratic basis functions on an unstructured grid is employed, and implemented via a highly adaptive characteristic-Galerkin scheme. The adaptivity of the code is illustrated on simplified test equations and finally for magnetic reconnection associated to the non linear development of the tilt instability between two repelling current channels. Varying the Lundquist number S, has allowed to study the transition between the steady-state Sweet-Parker reconnection regime (for S < ∼ 10 4 ) and plasmoids dominated reconnection one (for S > ∼ 10 5 ). The implications for the understanding of the mechanism explaining the fast conversion of free magnetic energy in astrophysical environments such as in solar corona are briefly discussed.

Balmer continuum enhancement detected in a mini flare observed with IRIS

“…The spectral signatures of the mini flare have been identified as IRIS bomb spectra (Peter et al 2014;Grubecka et al 2016;Young et al 2018;Joshi et al 2021). These structures can be due to plasmoid instablity, which creates tiny multi-thermal plasmoids that are not resolved by our telescopes (Ni et al 2016(Ni et al , 2021Baty 2019).…”

An adaptive scalable fully implicit algorithm based on stabilized finite element for reduced visco-resistive MHD

“…The above model has also been implemented recently in Ref. [27] for a continuous finiteelement implementation and the author pointed out that the challenge of B • ∇J in Ref.…”

“…[25] is based on a second-order finite-different algorithm and Ref. [27] uses a polynomial order of 1 or 2. In our implementation, we observed a very similar behavior around coarse-fine interfaces in AMR examples when the polynomial order is lower than 3.…”

“…Our goal is an algorithm to dynamically capture plasmoids in practical simulations as in [23,24], which requires an AMR capability that self-consistently evolves as localized plasmoids form and merge. To the best of our knowledge, the only works that successfully develop an implicit AMR approach for resistive MHD are [25][26][27]. Among those, only [27] was able to capture some plasmoids in the reconnection study of [24].…”

“…To the best of our knowledge, the only works that successfully develop an implicit AMR approach for resistive MHD are [25][26][27]. Among those, only [27] was able to capture some plasmoids in the reconnection study of [24]. The highest Lundquist number considered in Ref.…”