Unsteady Sediment‐Transport Modeling

The standard one‐dimensional equations of unsteady sediment‐transport are examined, and multiple time (or length) scales are identified. The existence of multiple scales may lead to a singularly perturbed behavior that should be taken into account in any general numerical model. Previous models, which reduce the number of conservation equations solved simultaneously from three to two, are seen to be unable to satisfy exactly either a general boundary condition or a general initial condition. Implications for numerical modeling are explored. Numerical results for the model problem of sediment‐deposition upstream of a dam illustrate the analytical argument.