Numerical simulations of dam-break flows of viscoplastic fluids via shallow water equations

Abstract

This paper presents simulations of dam-break flows of Herschel–Bulkley viscoplastic fluids over complex topographies using the shallow water equations (SWE). In particular, this study aims to assess the effects of rheological parameters: power-law index (n), consistency index (K), and yield stress (\(\tau _{c}\)), on 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 (downstream containing an initial fluid level). The effects of bed slope and depth ratios (the ratio between upstream and downstream fluid levels) on flow behaviour are also analyzed. The 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, peak height, and mean velocity decrease when any of the three rheological parameters are increased. However, based on a parametric sensitivity analysis, the power-law index appears to be the dominant factor in dictating fluid behaviour. Moreover, by increasing the bed slope and/or 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. This 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.