  In the present study, a characteristic-based boundary condition scheme is
developed for the compressible magnetohydrodynamic (MHD) equations in the
general curvilinear coordinate system, which is an extension of the
characteristic boundary scheme for the Navier-Stokes equations. The
eigenstructure and the complete set of characteristic waves are derived for the
ideal MHD equations in general curvilinear coordinates $(\xi, \eta, \zeta)$.
The characteristic boundary conditions are derived and implemented in a
high-order MHD solver where the sixth-order compact scheme is used for the
spatial discretization. The fifth-order Weighted Essentially Non-Oscillatory
(WENO) scheme is also employed for the spatial discretization of problems with
discontinuities. In our MHD solver, the fourth-order Runge-Kutta scheme is
utilized for time integration. The characteristic boundary scheme is first
verified for the non-magnetic (i.e., $\mathbf{B}=\textbf{0}$) Sod shock tube
problem. Then, various in-house test cases are designed to examine the derived
MHD characteristic boundary scheme for three different types of boundaries:
non-reflecting inlet and outlet, solid wall, and single characteristic wave
injection. The numerical examples demonstrate the accuracy and robustness of
the MHD characteristic boundary scheme.
