A central-constrained transport scheme for ideal magnetohydrodynamics

I propose an easy-to-code numerical scheme for the equations of compressible ideal magnetohydrodynamics (MHD) in multiple space dimensions. The presented method employs the central-upwind scheme of Kurganov et al. [SIAM J. Sci. Comput. 160 (2001) 707] in semi-discrete form combined with the constrained transport technique to satisfy the divergence-free condition for the magnetic field up to machine precision on the numerical grid. A variety of test problems in 1D, 2D and 3D show the robustness and efficiency of this 'hybrid ansatz' which renders it an interesting alternative to existing, numerically more intricate, solvers for the MHD equations. (C) 2003 Elsevier Inc. All rights reserved.