  The multiscale patch scheme is built from given small micro-scale simulations
of complicated physical processes to empower large macro-scale simulations. By
coupling small patches of simulations over unsimulated spatial gaps, large
savings in computational time are possible. Here we discuss generalising the
patch scheme to the case of wave systems on staggered grids in 2D space.
Classic macro-scale interpolation provides a generic coupling between patches
that achieves arbitrarily high order consistency between the emergent
macro-scale simulation and the underlying micro-scale dynamics. Eigen-analysis
indicates that the resultant scheme empowers feasible computation of large
macro-scale simulations of wave systems even with complicated underlying
physics. As examples we use the scheme to simulate some wave scenarios via a
turbulent shallow water model.
