Author(s): R. B. Canelas; R. M. L. Ferreira
Linked Author(s): Rui M.L. Ferreira
Keywords: Finite-volume; Mobile bed; Non-equilibrium transport; Adaptation length
Abstract: A novel two-dimensional depth-averaged mathematical model, applicable to discontinuous flows over complex mobile geometries is presented. It was derived within the shallow-flow hypothesis, and the mixture of fluid and granular material was idealized as a continuum. It features non-equilibrium sediment transport; the structure of the system of conservation laws is similar to its clear-water counterpart, since the imbalance between capacity and actual bedload discharge is a source term. The formulation for the latter requires a closure equation for the characteristic length describing a return-to-capacity length, an adaptation length. A new curve for the parameter is proposed. Closure equations are also needed for capacity sediment transport and for flow resistance. Dam-break flows do not generate alluvial bed forms, such as dunes. An upper-plane bed with a contact-load layer, saturating into fully developed debris-flow at the wave-front seems to be the dominant type of interaction between flow and bottom boundary. Energy dissipation in the contact-load layer can be idealized essentially as a consequence of inelastic binary collisions and long-lasting frictional contacts of sediment particles and fluid-particle viscous dissipation. Based on the work of Ferreira (2005), where the sheet-flow data of Sumer et al. (1996) was used to obtain a resistance formula applicable to dam-break flows, a variation of the same formulas are used. The particular nonequilibrium approach adopted in this work requires a closure equation for sediment transport at capacity conditions, whose conceptual model is based on the contact-load layer dynamics explored in Ferreira et al. (2009). The well-known formulas of Meyer-Peter and Muller and Bagnold are also employed and compared. The solution procedure was developed within the finite volume (FV) framework and based on the numerical discretization technique presented by Murillo and Garcia-Navarro (2010), Murillo et al. (2010) allowing for fully conservative solutions to initial-value problems. The discretization procedure of the non-homogeneous terms related to bed-slope leads to a wellbalanced scheme, allowing for a very robust method on the presence of violent changes in bottom geometry. A robust wetting–drying algorithm, entropy conditions to prevent nonphysical shocks and a revised Courant condition completes the numerical model. The model is novel in the sense that it combines a discretization technique developed and well tested for clear-water shallow-flow equations with a conceptual model built for unsteady flows over mobile beds featuring non-equilibrium sediment transport.