Multiscale modelling couples patches of non-linear wave-like simulations

Abstract

Given detailed microscale simulations of complicated physical processes, the multiscale gap-tooth scheme empowers efficient macroscale simulations. By coupling small patches of simulations over un-simulated physical gaps, large savings in computational time are possible. So far the gap-tooth scheme has been developed for dissipative systems, but wave-like systems arise in many applications. This article develops the gap-tooth scheme for the case of non-linear microscale simulations of wave-like systems. We show that 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. For example, 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, highly non-linear, wave-like dynamics with major computational savings.