A Godunov method for the computation of erosional shallow water transients

• Published in: International journal for numerical methods in fluids Vol. 41; no. 9; pp. 951 - 976
• Main Authors: Fraccarollo, L., Capart, H., Zech, Y.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 30.03.2003; Wiley
• Subjects: Applied sciences; Buildings. Public works; Computational methods in fluid dynamics; Dams and subsidiary installations; erosional dam-break problem; Exact sciences and technology; finite volume; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydraulic constructions; Physics; sediment transport; shallow-water equations; Transport equation; Dams; Ruptures; Computational fluid dynamics; Open channel flow; Digital simulation; Sediments; Finite volume methods; Shallow-water equations; Erosion
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.475

A Godunov method is proposed for the computation of open‐channel flows in conditions of rapid bed erosion and intense sediment transport. Generalized shallow water equations govern the evolution of three distinct interfaces: the water free‐surface, the boundary between pure water and a sediment transport layer, and the morphodynamic bottom profile. Based on the HLL scheme of Harten, Lax and Van Leer (1983), a finite volume numerical solver is constructed, then extended to second‐order accuracy using Strang splitting and MUSCL extrapolation. Lateralisation of the momentum flux is adopted to handle the non‐conservative product associated with bottom slope. Computational results for erosional dam‐break waves are compared with experimental measurements and semi‐analytical Riemann solutions. Copyright © 2003 John Wiley & Sons, Ltd.