High order interpolation methods for semi‐Lagrangian models of mobile‐bed hydrodynamics on Cartesian grids with cut cells

High order approximation methods based on radial basis functions are applied to the extension of semi‐Lagrangian shallow water models to staggered Cartesian meshes with cut boundary cells. The accuracy and efficiency of the resulting semi‐Lagrangian method is demonstrated by test cases simulating open channel flow. The derivative reconstruction provided by radial basis function interpolators is also employed successfully in the discretization of sediment transport models for mobile bed river flow. Copyright © 2005 John Wiley & Sons, Ltd.