  Block-to-block interface interpolation operators are constructed for several
common high-order finite difference discretizations. In contrast to
conventional interpolation operators, these new interpolation operators
maintain the strict stability, accuracy and conservation of the base scheme
even when nonconforming grids or dissimilar operators are used in adjoining
blocks. The stability properties of the new operators are verified using
eigenvalue analysis, and the accuracy properties are verified using numerical
simulations of the Euler equations in two spatial dimensions.
