Derivation and Numerical Resolution of 2D Shallow Water Equations for Multi-Regime Flows of Herschel-Bulkley Fluids

David, Michuri,; Monnier, Jérôme; Sellier, Mathieu

doi:10.2139/ssrn.4351903

Cited by 2 publications

(6 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The governing equations (2.1) -(2.4), are closed by defining appropriate boundary conditions for the free-surface and the basal topography. For the free-surface at z = H, we use the kinematic condition: The present study relies on the 1D version of the 2D SW model derived in [29]. The derivation is done by depth integration of the above equations applying the long-wave assumption.…”

Section: (B)mentioning

confidence: 99%

“…where S θ can be taken as S θ = sinθ, a zeroth-order approximation, or as S θ = sinθ − cosθ∂ x H, an improved approximation with a corrective slope term [29]. It is worth noting that the difference between the two terms only appear in areas of sharp changes of slopes as reported in [29]. The denominator D is given by…”

Section: (B)mentioning

confidence: 99%

“…To overcome such computational difficulties, reduced models such as the lubrication model and the Shallow Water Equations (SWEs) are usually adopted, see e.g. [2,[26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

“…Shallow Water (SW) like models are derived by depth integration assuming that the depth is much smaller than the characteristic length (the long-wave assumption). Only a few mathematically consistent SW flow models for Herschel-Bulkley fluids have been derived, see [2,29,30] and references therein. The present study conducts a parametric analysis of dam-break flows whose numerical computations rely on the flow model derived (and meticulously evaluated) in [29].…”

Section: Introductionmentioning

confidence: 99%

“…Only a few mathematically consistent SW flow models for Herschel-Bulkley fluids have been derived, see [2,29,30] and references therein. The present study conducts a parametric analysis of dam-break flows whose numerical computations rely on the flow model derived (and meticulously evaluated) in [29]. This model enables to take into account varying conditions at the bottom and wet dry front dynamics on non-flat topographies.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Muchiri

Hewett

Sellier

et al. 2023

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: (B)mentioning

confidence: 99%

Section: (B)mentioning

confidence: 99%

“…To overcome such computational difficulties, reduced models such as the lubrication model and the Shallow Water Equations (SWEs) are usually adopted, see e.g. [2,[26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Muchiri

Hewett

Sellier

et al. 2023

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

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

Muchiri,

Hewett,

Sellier

et al. 2024

Theor. Comput. Fluid Dyn.

View full text Add to dashboard Cite

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 ($$\tau _{c}$$ τ 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. Graphical abstract

show abstract

Derivation and Numerical Resolution of 2D Shallow Water Equations for Multi-Regime Flows of Herschel-Bulkley Fluids

Cited by 2 publications

References 29 publications

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

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

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

Contact Info

Product

Resources

About