This study presents a novel, simple, but rather accurate approximation of the eigenvalues of the system formed by the Saint-Venant–Exner equations, based on the comparison between eigenvalues for the complete system and eigenvalues for the water phase only. Moreover, a strategy is proposed to compute efficiently the intercell fluxes by properly adapting a Harten, Lax, and van Leer scheme for each equation. Two examples of transient transcritical flows are developed: the erosive migration of a knickpoint induced by an increase in the bed slope, and the evolution of a hydraulic jump over a mobile bed.
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Goutière et al. (2008) studied this question.
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