A localized differential quadrature model for moving boundary shallow water flows.

This work presents a novel numerical solution of nonlinear shallow water equations involving moving waterlines. A hybrid Lagrangian–Eulerian mapping technique was proposed to account for two simultaneous shorelines fluctuating over dry beds. In the numerical model developed in this study, the local differential quadrature method approximated the spatial derivatives and the real-time Adams–Moulton algorithm was implemented for time-marching. It was concluded that, despite using significantly small number of grid points, the model leads to accurate results compared with an existing finite volume model which demands comparatively finer meshes. Further, highly accurate predictions of the position and velocity of the moving shorelines were obtained which is considered as the key advantage of the Lagrangian shoreline tracking. [ABSTRACT FROM PUBLISHER]