1D finite volume model of unsteady flow over mobile bed

Abstract

Summary A one dimensional (1D) finite volume method (FVM) model was developed for simulating unsteady flow, such as dam break flow, and flood routing over mobile alluvium. The governing equation is the modified 1D shallow water equation and the Exner equation that take both bed load and suspended load transport into account. The non-equilibrium sediment transport algorithm was adopted in the model, and the van Rijn method was employed to calculate the bed-load transport rate and the concentration of suspended sediment at the reference level. Flux terms in the governing equations were discretised using the upwind flux scheme, Harten et al. (1983) (HLL) and HLLC schemes, Roe’s scheme and the Weighted Average Flux (WAF) schemes with the Double Minmod and Minmod flux limiters. The model was tested under a fixed bed condition to evaluate the performance of several different numerical schemes and then applied to an experimental case of dam break flow over a mobile bed and a flood event in the Rillito River, Tucson, Arizona. For dam break flow over movable bed, all tested schemes were proved to be capable of reasonably simulating water surface profiles, but failed to accurately capture the hydraulic jump. The WAF schemes produced slight spurious oscillations at the water surface and bed profiles and over-estimated the scour depth. When applying the model to the Rillito River, the simulated results generally agreed well with the field measurements of flow discharges and bed elevation changes. Modeling results of bed elevation changes were sensitive to the suspended load recovery coefficient and the bed load adaptation length, which require further theoretical and experimental investigations.