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The multiscale gap-tooth scheme is built from given microscale simulations ofcomplicated physical processes to empower macroscale simulations. By couplingsmall patches of simulations over unsimulated physical gaps, large savings incomputational time are possible. So far the gap-tooth scheme has been developedfor dissipative systems, but wave systems are also of great interest. Thisarticle develops the gap-tooth scheme to the case of nonlinear microscalesimulations of wave-like systems. Classic macroscale interpolation provides ageneric coupling between patches that achieves arbitrarily high orderconsistency between the multiscale scheme and the underlying microscaledynamics. Eigen-analysis indicates that the resultant gap-tooth scheme empowersfeasible computation of large scale simulations of wave-like dynamics withcomplicated underlying physics. As an pilot study, we implement numericalsimulations of dam-breaking waves by the gap-tooth scheme. Comparison between agap-tooth simulation, a microscale simulation over the whole domain, and somepublished experimental data on dam breaking, demonstrates that the gap-toothscheme feasibly computes large scale wave-like dynamics with computationalsavings.

Multiscale modelling couples patches of nonlinear wave-like simulations