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Magnetic field in the solar corona is usually extrapolated from photosphericvector magnetogram using a nonlinear force-free field (NLFFF) model. NLFFFextrapolation needs a considerable effort to be devoted for its numericalrealization. In this paper we present a new implementation of themagnetohydrodynamics (MHD)-relaxation method for NLFFF extrapolation. Themagneto-frictional approach which is introduced for speeding the relaxation ofthe MHD system is novelly realized by the spacetime conservation-element andsolution-element (CESE) scheme. A magnetic field splitting method is used tofurther improve the computational accuracy. The bottom boundary condition isprescribed by changing the transverse field incrementally to match themagnetogram, and all other artificial boundaries of the computational box aresimply fixed. We examine the code by two types of NLFFF benchmark tests, theLow & Lou (1990) semi-analytic force-free solutions and a more realisticsolar-like case constructed by van Ballegooijen et al. (2007). The results showthat our implementation are successful and versatile for extrapolations ofeither the relatively simple cases or the rather complex cases which needsignificant rebuilding of the magnetic topology, e.g., a flux rope. We alsocompute a suite of metrics to quantitatively analyze the results anddemonstrate that the performance of our code in extrapolation accuracybasically reaches the same level of the present best-performing code, e.g.,that developed by Wiegelmann (2004).

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