Numerical simulations of dam-break flows of viscoplastic fluids via Shallow Water equations

Abstract This paper presents simulations of channelized dam-break flows of Herschel–Bulkley viscoplastic fluids over complex topographies using the Shallow Water equations (SWEs). Particularly, the study aims at assessing the effects of rheological parameters: power-law index (n), consistency index (K) and yield stress (\tau_{c}), on the flow height and velocity over different topographies. Three practical examples of dam-break flow cases are considered: a dam-break on an inclined flat surface, a dam-break over a non-flat topography, and a dam-break over a wet bed. Effects of the bed slope and depth ratios between upstream and downstream fluid levels, on the flow behaviour are also analyzed. Numerical results are compared with experimental data from the literature, and are found to be in good agreement. Results show that for both dry and wet bed conditions, the fluid front position, the peak height, and mean velocity decrease when any of the three rheological parameters is increased. However, based on parametric sensitivity analysis, the power-law index appears to be the dominant factor in dictating the fluid behaviour. Moreover, increasing the bed slope and/or the depth ratio, the wave frontal position moves further downstream. Furthermore, the presence of an obstacle is observed to cause the formation of an upsurge that moves in the upstream direction; which increases by increasing any of the three rheological parameters. The study is useful for an in-depth understanding of the effects of rheology on catastrophic gravity driven flows of non-Newtonian fluids (like lava or mud flows) for risk assessment and mitigation.