  The multiscale gap-tooth scheme is built from given microscale simulations of
complicated physical processes to empower macroscale simulations. By coupling
small patches of simulations over unsimulated physical gaps, large savings in
computational time are possible. So far the gap-tooth scheme has been developed
for dissipative systems, but wave systems are also of great interest. This
article develops the gap-tooth scheme to the case of nonlinear microscale
simulations of wave-like systems. Classic macroscale interpolation provides a
generic coupling between patches that achieves arbitrarily high order
consistency between the multiscale scheme and the underlying microscale
dynamics. Eigen-analysis indicates that the resultant gap-tooth scheme empowers
feasible computation of large scale simulations of wave-like dynamics with
complicated underlying physics. As an pilot study, we implement numerical
simulations of dam-breaking waves by the gap-tooth scheme. Comparison between a
gap-tooth simulation, a microscale simulation over the whole domain, and some
published experimental data on dam breaking, demonstrates that the gap-tooth
scheme feasibly computes large scale wave-like dynamics with computational
savings.
