  A methodology for handling block-to-block coupling of nonconforming,
multiblock summation-by-parts finite difference methods is proposed. The
coupling is based on the construction of projection operators that move a
finite difference grid solution along an interface to a space of piecewise
defined functions; we specifically consider discontinuous, piecewise polynomial
functions. The constructed projection operators are compatible with the
underlying summation-by-parts energy norm. Using the linear wave equation in
two dimensions as a model problem, energy stability of the coupled numerical
method is proven for the case of curved, nonconforming block-to-block
interfaces. To further demonstrate the power of the coupling procedure, we show
how it allows for the development of a provably energy stable coupling between
curvilinear finite difference methods and a curved-triangle discontinuous
Galerkin method. The theoretical results are verified through numerical
simulations on curved meshes as well as eigenvalue analysis.
