A semi-Lagrangian method of characteristics for the shallow-water equations

In this paper a fully explicit semi-Lagrangian method of characteristics for the one-dimensional shallow-water equations is developed. The method is explicit and unconditionally stable. The amplitude and phase speed properties for gravity-wave motions are very accurate even for long time steps. The central idea is to use the semi-Lagrangian approach on the so-called characteristic equations. It is also shown that if an explicit semi-Lagrangian scheme is used for hyperbolic systems of equations, then the scheme should be applied to the characteristic equations of the system in order to guarantee a stable and consistent treatment of wave motions (more generally, this is true for any explicit upwind-biased scheme).