A 1D numerical model for the simulation of unsteady and highly erosive flows in rivers

Abstract

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Exploring different possibilities for second‐order well‐balanced Lagrange‐projection numerical schemes applied to shallow water Exner equations

“…Moreover, we take , cells and s as ending time. We refer to the works 11,15 for more details and for the analytical solutions reported in Figures 3–5. In particular, we plot the free surface and bed elevation outputs using both first and second order method.…”

“…In particular, the first one is based on a fully coupled approach while the second one consists in a decoupled strategy where the oscillations are in part stabilized by controlling the stability region. Without being exhaustive, see for instance References 14‐16 for further coupled schemes applied to the shallow water Exner system.…”

“…Finally, represents the time and x the axial coordinate. In compact form, we have where For more details about shallow‐water equations with and without moving topography, we refer for instance to References 4,12,15,17‐24. Let us know focus on the solid transport discharge , which can be formulated in different ways depending on the characteristics of the sediment and the flow, see for instance Reference 25.…”

A new form of the Saint-Venant equations for variable topography

“…One-dimensional (1D) hydrodynamic models using the Saint-Venant equations (SVEs) are widely employed for studying both natural streams and man-made channels (e.g., Martinez-Aranda et al, 2019;Sanders, 2001). It is widely recognized that numerical solutions of the SVEs are prone to spurious oscillations in the free-surface elevation unless particular care is taken in the numerical formulation and/or the problem definition (e.g., Nujic, 1995;Tseng, 2004).…”

A new form of the Saint–Venant equations for variable topography

“…One-dimensional (1D) hydrodynamic models using the Saint-Venant equations (SVE) are widely employed for studying both 90 natural streams and man-made channels (e.g., Martinez-Aranda et al, 2019;Sanders, 2001). It is widely recognized that numerical solutions of the SVE are prone to spurious oscillations in the free-surface elevation unless particular care is taken in the numerical formulation and/or the problem definition (e.g., Nujic, 1995;Tseng, 2004).…”