HLLC scheme with novel wave-speed estimators appropriate for two-dimensional shallow-water flow on erodible bed
(2011) International Journal for Numerical Methods in Fluids — Vol. 66, n° 9, p. 1019-1036 (2011)
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- Abstract
- This paper presents a first-order HLLC (Harten-Lax-Van Leer with contact discontinuities) scheme to solve the Saint-Venant shallow-water equations, including morphological evolution of the bed by erosion and deposition of sediments. The Exner equation is used to model the morphological evolution of the bed, while a closure equation is needed to evaluate the rate of sediment transport. The system of Saint- Venant–Exner equations is solved in a fully coupled way using a finite-volume technique and a HLLC solver for the fluxes, with a novel wave-speed estimator adapted to the Exner equation. Wave speeds are usually derived by computing the eigenvalues of the full system, which is highly time-consuming when no analytical expression is available. In this paper, an eigenvalue analysis of the full system is conducted, leading to simple but still accurate wave-speed estimators. The new numerical scheme is then tested in three different situations: (1) a circular dam-break flow over movable bed, (2) an one-dimensional bed aggradation problem simulated on a 2D unstructured mesh and (3) the case of a dam-break flow in an erodible channel with a sudden enlargement, for which experimental measurements are available.
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Soares Frazao, S., & Zech, Y. (2011). HLLC scheme with novel wave-speed estimators appropriate for two-dimensional shallow-water flow on erodible bed. International Journal for Numerical Methods in Fluids, 66(9), 1019-1036. https://doi.org/10.1002/fld.2300 (Original work published 2011)