Modeling Alluvial Channel Bed Transients

A mathematical model is developed to simulate bed transient formation and propagation in alluvial channels. The model is of the known-discharge type, i.e., within one time step, the water discharge is considered steady. This technique allows for the implicit numerical modeling of bed transient propagation using longer time steps that would otherwise be possible using the conventional sequential routing method. Instability due to ill-posing of the sediment transport function is circumvented by using a power relation between bed material transport and mean flow velocity. Errors in mass conservation due to linearization at the boundary are eliminated by using a nonlinear formulation of the upstream boundary condition.