A new computational framework for one-dimensional mobile-bed simulation has been developed. The approach is based on use of the full de St. Venant flow equations, treatment of sediment mixtures, recognition of the distinctly different physics of suspended load and bedload movement, use of a spatial-delay loading law for bedload, and fully coupled, implicit numerical solution of the resulting set of partial-differential equations. In eliminating most of the conceptual and numerical weaknesses of existing methods, the new approach establishes a new standard of fidelity to the governing conservation laws, whatever be the particular empirical sediment relations employed for a particular application. A companion article presents test applications of the method.
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