  Curvilinear, multiblock summation-by-parts finite difference operators with
the simultaneous approximation term method provide a stable and accurate
framework for solving the wave equation in second order form. That said, the
standard method can become arbitrarily stiff when characteristic boundary
conditions and nonlinear interface conditions are used. Here we propose a new
technique that avoids this stiffness by using characteristic variables to
"upwind" the boundary and interface treatment. This is done through the
introduction of an additional block boundary displacement variable. Using a
unified energy, which expresses both the standard as well as characteristic
boundary and interface treatment, we show that the resulting scheme has
semidiscrete energy stability for the scalar anisotropic wave equation. The
theoretical stability results are confirmed with numerical experiments that
also demonstrate the accuracy and robustness of the proposed scheme. The
numerical results also show that the characteristic scheme has a time step
restriction based on standard wave propagation considerations and not the
boundary closure.
