A New Implementation of the Magnetohydrodynamics-Relaxation Method for Nonlinear Force-Free Field Extrapolation in the Solar Corona

Magnetic field in the solar corona is usually extrapolated from photospheric vector magnetogram using a nonlinear force-free field (NLFFF) model. NLFFF extrapolation needs a considerable effort to be devoted for its numerical realization. In this paper we present a new implementation of the magnetohydrodynamics (MHD)-relaxation method for NLFFF extrapolation. The magneto-frictional approach which is introduced for speeding the relaxation of the MHD system is novelly realized by the spacetime conservation-element and solution-element (CESE) scheme. A magnetic field splitting method is used to further improve the computational accuracy. The bottom boundary condition is prescribed by changing the transverse field incrementally to match the magnetogram, and all other artificial boundaries of the computational box are simply fixed. We examine the code by two types of NLFFF benchmark tests, the Low & Lou (1990) semi-analytic force-free solutions and a more realistic solar-like case constructed by van Ballegooijen et al. (2007). The results show that our implementation are successful and versatile for extrapolations of either the relatively simple cases or the rather complex cases which need significant rebuilding of the magnetic topology, e.g., a flux rope. We also compute a suite of metrics to quantitatively analyze the results and demonstrate that the performance of our code in extrapolation accuracy basically reaches the same level of the present best-performing code, e.g., that developed by Wiegelmann (2004).