A grid-free, nonlinear shallow-water model with moving boundary

A meshless method based on the radial basis function is derived to solve the nonlinear, nondispersive shallow-water equations. The one-dimensional initial boundary value problem has a fixed boundary at one end and a free boundary at the other. The formulation employs a Lagrangian-Eulerian scheme to track the movement of the free boundary and transform the problem to a time-independent domain. The radial basis function evaluates the spatial derivatives in the numerical solution, while the Wilson-θ method integrates the development of the flow in time. The model is applied to calculate the flow of floodwater resulting from dam collapse and the run-up of waves on a plane beach. Comparisons of the computed results with analytical and finite difference solutions demonstrate the accuracy and capability of this meshless model in engineering applications. © 2004 Elsevier Ltd. All rights reserved.