Lagrangian Modeling of the Dynamics of River and Floodplain Flow

Abstract

A new Lagrangian, dynamic river model is described. The model solves the coupled one-dimensional hydrostatic flow equations separately in a main river channel and in adjacent floodplains using a two-stage predictor-corrector scheme. The lateral interaction between the main channel and floodplains, due to both advective exchange arising from lateral pressure gradients and turbulent exchange due to lateral shear, is included. The Lagrangian moving grid eliminates numerical diffusion and oscillations commonly experienced in Eulerian models, and can accurately simulate wave propagation and nonlinear steepening until wave breaking. The Lagrangian moving grid is dynamically adaptive, providing variable resolution as the moving fluid parcel’s length changes, either because the cross-sectional flow area or the flow depth changes as the wave moves down a channel of variable cross section. The model also allows flows over dry beds and moving boundaries to be handled efficiently. The model was successfully validated for a flow induced by a simple wave in a prismatic channel, flood waves in laboratory compound channels, and flow in a natural river.