A fully implicit numerical method for single-fluid resistive magnetohydrodynamics Daniel R. Reynolds a, * , Ravi Samtaney b , Carol S. Woodward c a Department of Mathematics, University of California at San Diego, 9500 Gilman Drive, Dept 0112, La Jolla, San Diego, CA 92093-0112, United States b Princeton Plasma Physics Lab, MS 26, P.O. Box 451, Princeton, NJ 08543, United States c Lawrence Livermore National Lab, P.O. Box 808, L-551, Livermore, CA 94551, United States Received 13 May 2005; received in revised form 4 March 2006; accepted 18 March 2006 Available online 11 May 2006 Abstract We present a nonlinearly implicit, conservative numerical method for integration of the single-fluid resistive MHD equations. The method uses a high-order spatial discretization that preserves the solenoidal property of the magnetic field. The fully coupled PDE system is solved implicitly in time, providing for increased interaction between physical processes as well as additional stability over explicit-time methods. A high-order adaptive time integration is employed, which in many cases enables time steps ranging from one to two orders of magnitude larger than those constrained by the explicit CFL condition. We apply the solution method to illustrative examples relevant to stiff magnetic fusion processes which chal- lenge the efficiency of explicit methods. We provide computational evidence showing that for such problems the method is comparably accurate with explicit-time simulations, while providing a significant runtime improvement due to its increased temporal stability. Ó 2006 Elsevier Inc. All rights reserved. Keywords: Newton–Krylov; Implicit couplings; Resistive magnetohydrodynamics 1. Introduction 1.1. Motivation The design of next-generation magnetic fusion devices requires increased understanding of nonlinear mac- roscopic stability, reconnection processes and refueling approaches for burning plasmas. Due to the high cost of conducting physical experiments of these processes in magnetic fusion devices, researchers are increasingly turning to computational simulation as a tool for such scientific investigation. However, it is well known that 0021-9991/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jcp.2006.03.022 * Corresponding author. Tel.: +1 858 534 5862; fax: +1 858 534 5273. E-mail addresses: drreynolds@ucsd.edu (D.R. Reynolds), samtaney@pppl.gov (R. Samtaney), cswoodward@llnl.gov (C.S. Woodward). Journal of Computational Physics 219 (2006) 144–162 www.elsevier.com/locate/jcp