On a numerical strategy to compute gravity currents of non-Newtonian fluids

Tsunamis caused by landslides may result in significant destruction of the surroundings with both societal and industrial impact. The 1958 Lituya Bay landslide and tsunami is a recent and well-documented terrestrial landslide generating a tsunami with a run-up of 524 m. Although recent computational techniques have shown good performance in the estimation of the run-up height, they fail to capture all the physical processes, in particular, the landslide-entry profile and interaction with the water. Smoothed particle hydrodynamics (SPH) is a versatile numerical technique for describing free-surface and multi-phase flows, particularly those that exhibit highly nonlinear deformation in landslide-generated tsunamis. In the current work, the novel multi-phase incompressible SPH method with shifting is applied to the Lituya Bay tsunami and landslide and is the first methodology able to reproduce realistically both the run-up and landslide-entry as documented in a benchmark experiment. The method is the first paper to develop a realistic implementation of the physics that in addition to the non-Newtonian rheology of the landslide includes turbulence in the water phase and soil saturation. Sensitivity to the experimental initial conditions is also considered. This work demonstrates the ability of the proposed method in modelling challenging environmental multi-phase, non-Newtonian and turbulent flows.

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“…The stress tensor τ for inelastic non-Newtonian flows is given by the following constitutive law [39]:…”

Section: (C) Viscous Termsmentioning

confidence: 99%

“…where |D| is the second principal invariant of the shear strain rate, D = ∇u + ∇u T , [39]: shear strain rate tensor can be written as…”

Section: (C) Viscous Termsmentioning

confidence: 99%

Landslides and tsunamis predicted by incompressible smoothed particle hydrodynamics (SPH) with application to the 1958 Lituya Bay event and idealized experiment

et al. 2017

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“…[34], [38,37], [25], [36], [26]) is that they use decomposition-coordination methods to solve the variational inequality associated to constitutive laws with a so-called plastic threshold (the most simple and iconic one being the Bingham model). This kind of approach takes its roots in the seminal works of Duvaut-Lions [15] and the series of papers of Glowinski and coworkers (see the recent book [23] for a detailed review), initiated at the end of the seventies and anchored in the Augmented Lagrangian formalism.…”

Section: Introductionmentioning

confidence: 99%

Efficient numerical schemes for viscoplastic avalanches. Part 2: The 2D case

Fernández-Nieto

Gallardo

Vigneaux

2018

Journal of Computational Physics

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This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated to the yield threshold: finite-volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez-Moreno) to discretize the problem. To be able to accurately simulate the stopping behaviour of the avalanche, new schemes need to be designed, involving the classical notion of wellbalancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. We derived such schemes and numerical experiments are presented to show their performances.

show abstract

“…[33], [37,36], [24], [35], [25]) is that they use decomposition-coordination methods to solve the variational inequality associated to constitutive laws with a so-called plastic threshold (the most simple and iconic one being the Bingham model). This kind of approach takes its roots in the seminal works of Duvaut-Lions [15] and the series of papers of Glowinski and coworkers (see the recent book [22] for a detailed review), initiated at the end of the seventies and anchored in the Augmented Lagrangian formalism.…”

Section: Introductionmentioning

confidence: 99%

Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case

Fernández-Nieto

Gallardo

Vigneaux

2014

Journal of Computational Physics

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This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated to the yield threshold: finitevolume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez-Moreno) to discretize the problem. To be able to accurately simulate the stopping behaviour of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. We derived such schemes and numerical experiments are presented to show their performances.

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On a numerical strategy to compute gravity currents of non-Newtonian fluids

Cited by 40 publications

References 25 publications

Landslides and tsunamis predicted by incompressible smoothed particle hydrodynamics (SPH) with application to the 1958 Lituya Bay event and idealized experiment

Landslides and tsunamis predicted by incompressible smoothed particle hydrodynamics (SPH) with application to the 1958 Lituya Bay event and idealized experiment

Efficient numerical schemes for viscoplastic avalanches. Part 2: The 2D case

Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case

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