Explicit radial basis function collocation method for computing shallow water flows

Abstract

A simple Explicit Radial Basis Function (RBF) is used to solve the shallow water equations (SWEs) for flows over irregular, frictional topography involving wetting and drying. At first we construct the MQ-RBF interpolation corresponding to space derivative operators. Next, we obtain numerical schemes to solve the SWEs, by using the gradient of the interpolant to approximate the spatial derivative of the differential equation and a third-order explicit Runge-Kutta scheme to approximate the temporal derivative of the differential equation. Then, we verify our scheme against several idealized one-dimensional numerical experiments including dam-break and open channel flows over non-uniform beds (involving shock wave behavior), and moving wet-dry fronts over irregular bed topography. Promising results are obtained.