  In this paper a characteristics-based open boundary condition (CBC) is
proposed for the magnetohydrodynamic (MHD) system of equations. The algorithm
is carefully designed and implemented in the context of a high-order flux
reconstruction (FR) scheme under the Generalized Lagrange Multiplier (GLM)-MHD
system of equations. It is implemented by adding the contribution of the
characteristic equation directly to the corrected flux term in the FR scheme
dispensing with solving time-dependent characteristic equations along boundary
faces. The CBC method is shown to be more accurate and robust than commonly
used zero normal derivative (ZND) and approximate Riemann solver boundary
conditions (ARBC) in solving 1D, 2D, and 3D test problems. The CBC method is
successfully applied to simulate challenging problems of magnetic reconnection
for which other options failed to get stable results over long-period time
integration.
