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|Title:||Multiscale modelling couples patches of non-linear wave-like simulations|
|Citation:||IMA Journal of Applied Mathematics, 2016; 81(2):228-254|
|Publisher:||Oxford University Press|
|Meng Cao and A.J. Roberts|
|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 unsimulated 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.|
|Keywords:||PDEs; multi-scale model; gap-tooth scheme; nonlinear water wave; dam breaking|
|Rights:||© The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.|
|Appears in Collections:||Mathematical Sciences publications|
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