Parallel adaptive numerical simulation of dry avalanches over natural terrain

Patra, Abani; Bauer, Andy; Nichita, C.C.; Pitman, E. Bruce; Sheridan, M. F.; Bursik, Marcus; Rupp, B.; Webber, Andrew; Stinton, A.; Namikawa, Laércio Massaru; Renschler, Chris S.

doi:10.1016/j.jvolgeores.2004.06.014

Cited by 244 publications

(244 citation statements)

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“…Wang et al (2004) made a careful study investigating its optimal use in avalanche studies of the extended Savage-Hutter equations. For alternative numerical schemes also see Iverson (2001, 2004), Koschdon and Schäfer (2003), Iverson et al (2004), Patra et al (2005) and Vollmöller (2004).…”

Section: Numerical Integration Techniquesmentioning

confidence: 99%

“…Mathematically, the present formulation adopts an orthogonal coordinate system along a curved and twisted master curve (see that is suggested by the thalweg of the valley or corrie, through which the debris flow takes place. This is advantageous and preferable to the horizontal and vertical coordinates used by others (see, e.g., Hungr, 1995;Iverson andDenlinger, 2001, 2004;Zwinger et al, 2003;Pitman et al, 2003;Patra et al, 2005), because it is more naturally adjusted to the geometries which one often encounters in debris flows -and it is more accurate whenever slopes are large (30 • -50 • ) and the mountain valley is generally curved and twisted. In fact, a mathematically correct asymptotic analysis cannot rigorously be performed if the coordinates are not following the topography.…”

Section: Introductionmentioning

confidence: 99%

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Modelling debris flows down general channels

Pudasaini

Wang

Hutter

2005

Nat. Hazards Earth Syst. Sci.

167

160

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Abstract. This paper is an extension of the single-phase cohesionless dry granular avalanche model over curved and twisted channels proposed by . It is a generalisation of the Hutter (1989, 1991) equations based on simple channel topography to a twophase fluid-solid mixture of debris material. Important terms emerging from the correct treatment of the kinematic and dynamic boundary condition, and the variable basal topography are systematically taken into account. For vanishing fluid contribution and torsion-free channel topography our new model equations exactly degenerate to the previous Savage-Hutter model equations while such a degeneration was not possible by the Iverson and Denlinger (2001) model, which, in fact, also aimed to extend the Savage and Hutter model. The model equations of this paper have been rigorously derived; they include the effects of the curvature and torsion of the topography, generally for arbitrarily curved and twisted channels of variable channel width. The equations are put into a standard conservative form of partial differential equations. From these one can easily infer the importance and influence of the pore-fluid-pressure distribution in debris flow dynamics. The solid-phase is modelled by applying a Coulomb dry friction law whereas the fluid phase is assumed to be an incompressible Newtonian fluid. Input parameters of the equations are the internal and bed friction angles of the solid particles, the viscosity and volume fraction of the fluid, the total mixture density and the pore pressure distribution of the fluid at the bed. Given the bed topography and initial geometry and the initial velocity profile of the debris mixture, the model equations are able to describe the dynamics of the depth profile and bed parallel depth-averaged velocity distribution from the initial position to the final deposit. A shock capturing, total variation diminishing numerical scheme is implemented to solve the highly non-linear equations. Simulation results present the combined effects of curvature, torsion and pore pressureCorrespondence to: S. P. Pudasaini (pudasain@mechanik.tu-darmstadt.de) on the dynamics of the flow over a general basal topography. These simulation results reveal new physical insight of debris flows over such non-trivial topography. Model equations are applied to laboratory avalanche and debris-flow-flume tests. Very good agreement between the theory and experiments is established.

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Section: Numerical Integration Techniquesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modelling debris flows down general channels

Pudasaini

Wang

Hutter

2005

Nat. Hazards Earth Syst. Sci.

167

160

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“…The Titan2D computer program (Pitman et al, 2003;Patra et al, 2005) was designed by the Geophysical Mass Flow Modeling Group at University at Buffalo, USA, to simulate dry granular avalanches over digital representations of natural terrain. The program is built on a depth-averaged model for an incompressible Coulomb continuum, a "shallow water" granular flow, based on the work of Savage & Hutter (1989), Iverson (1997), , and Mangeney-Castelnau et al (2002).…”

Section: Titan2dmentioning

confidence: 99%

“…Recent advances have been made in creating computational models of gravity-driven flows using the shallow-water approximation for the purpose of hazard mitigation (e.g., McEwen & Malin, 1989;Takahashi & Tsujimoto, 2000;Patra et al, 2005). Applications of these models have been used for block-andash flows at several volcanoes including Colima, El Chichon and Nevado de Toluca volcanoes in Mexico Patra et al, 2005;Saucedo et al, 2005;Rupp et al, 2006;Macias et al, 2008;Sulpizio et al, 2010); Mount Taranaki, New Zealand (Procter et al, 2010); Tungurahua, Ecuador (Kelfoun et al, 2009); Galeras and El Chichon Volcano, Columbia (Stefanescu et al, 2009;Murcia et al, 2010); Arenal Volcano, Costa Rica (Berrocal & Malavassi, 2006); Soufrière Hills Volcano, Montserrat (Hidayat et al, 2007;Ogburn, 2008;Ogburn et al, in press); and Merapi Volcano, Indonesia (Itoh, 2000;Charbonnier & Gertisser, 2009, 2012.…”

Section: Introductionmentioning

confidence: 99%

“…As the complexities of the flow mechanics and interactions are far from being fully understood, shallow-water models rely upon simplified rheological laws that have been tested in both the laboratory and natural examples (e.g., Patra et al, 2005;Kelfoun et al, 2009). Such models are either based on frictional (Mohr-Coulomb) behavior (the Titan2D model developed at the University at Buffalo, USA) or other rheological laws (e.g., constant shear).…”

Section: Introductionmentioning

confidence: 99%

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Aplicación de modelos numéricos de "aguas someras" para el análisis de peligros de flujos volcánicos: El caso de Titan2D y volcán Turrialba (Costa Rica)

Charbonnier

Palma

Ogburn

2015

Rev. Geol. Amér. Central

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This paper introduces Titan2D, a depth averaged model of an incompressible Coulomb continuum for "shallow water" granular flows. Titan2D has been used successfully at many volcanoes to predict inundation by blockand-ash flows and debris avalanches. It can be run as a stand-alone program or through Vhub, a cyber-infrastructure platform. Practical considerations of choosing appropriate user inputs and the basics of running the model are discussed herein. Both synthetic and natural terrain examples are presented, including simulations of a block-and-ash flow generated from the gravitational collapse of a synthetic dome at Turrialba volcano (Costa Rica). These results suggest that the model should be limited to simulate cases of dense volcanic granular flows, like those produced by gravity-driven dome collapse events, but cannot be used to simulate dilute pyroclastic density currents. Finally, estimation of the Titan2D resistance terms by using empirical relationships provides a good method for reducing model input uncertainties.

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A two‐layer depth‐averaged model for both the dilute and the concentrated parts of pyroclastic currents

Kelfoun

2017

JGR Solid Earth

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Pyroclastic currents are very destructive and their complex behavior makes the related hazards difficult to predict. A new numerical model has been developed to simulate the emplacement of both the concentrated and the dilute parts of pyroclastic currents using two coupled depth‐averaged approaches. Interaction laws allow the concentrated current (pyroclastic flow) to generate a dilute current (pyroclastic surge) and, inversely, the dilute current to form a concentrated current or a deposit. The density of the concentrated current is assumed to be constant during emplacement, whereas the density of the dilute current changes depending on the particle supply from the concentrated current and the mass lost through sedimentation. The model is explored theoretically using simplified geometries as proxies for natural source conditions and topographies. It reproduces the relationships observed in the field between the surge genesis and the topography: the increase in surge production in constricted valleys, the decoupling between the concentrated and the dilute currents, and the formation of surge‐derived concentrated flows. The strong nonlinear link between the surge genesis and the velocity of the concentrated flow beneath it could explain the sudden occurrence of powerful and destructive surges and the difficulty of predicting this occurrence. A companion paper compares the results of the model with the field data for the eruption of Merapi in 2010 and demonstrates that the approach is able to reproduce the natural emplacement of the concentrated and the dilute pyroclastic currents studied with good accuracy.

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Parallel adaptive numerical simulation of dry avalanches over natural terrain

Cited by 244 publications

References 13 publications

Modelling debris flows down general channels

Modelling debris flows down general channels

Aplicación de modelos numéricos de "aguas someras" para el análisis de peligros de flujos volcánicos: El caso de Titan2D y volcán Turrialba (Costa Rica)

A two‐layer depth‐averaged model for both the dilute and the concentrated parts of pyroclastic currents

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