A Computational Model for Simulation of Shallow Water Waves by Elastic Deformations in the Topography (Communications in Computational Physics, 2021)
We propose a coupled model to simulate shallow water waves induced byelastic deformations in the bed topography. The governing equations consist of thedepth-averaged shallow water equations including friction terms for the water free-surface and the well-known second-order elastostatics formulation for the bed deformation. The perturbation on the free-surface is assumed to be caused by a suddenchange in the bottom beds. At the interface between the water flow and the bed topography, transfer conditions are implemented. Here, the hydrostatic pressure andfriction forces are considered for the elastostatic equations whereas bathymetric forcesare accounted for in the shallow water equations. The focus in the present study is onthe development of a simple and accurate representation of the interaction betweenwater waves and bed deformations in order to simulate practical shallow water flowswithout relying on complex partial differential equations with free boundary conditions. The effects of location and magnitude of the deformation on the flow fields andfree-surface waves are investigated in details. Numerical simulations are carried outfor several test examples on shallow water waves induced by sudden changes in thebed. The proposed computational model has been found to be feasible and satisfactory.