Modelling rapid mass movements using the shallow water equations in Cartesian coordinates

Hergarten, Stefan; Robl, Jörg

doi:10.5194/nhess-15-671-2015

Cited by 31 publications

(38 citation statements)

References 24 publications

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“…The boundary condition u · n b = 0 (28) ensures that the velocity of the fluid is surface-tangential, as assumed by the boundary layer approximation and the Savage-Hutter model. This constraint can be considered as an equation to determine basal pressure p b in every point of the surface.…”

Section: Topography Boundary Conditionmentioning

confidence: 99%

“…Therefore, further extensions have been proposed by introducing a superimposed shallow terrain [24], a twisted central flow path [25], and curvature effects on friction [12]. In addition, a description in Cartesian coordinates, similar to the Shallow Water Equations, has been investigated [26,27,28], taking into account the inclination with various correction terms.…”

Section: Introductionmentioning

confidence: 99%

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A finite area scheme for shallow granular flows on three-dimensional surfaces

Rauter

Tuković

2018

Computers & Fluids

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Shallow flow or thin liquid film models are used for a wide range of physical and engineering problems. They are applicable to free surface flows, when the flow thickness is distinctly smaller than the lateral dimension. Respective situations exist in automotive and aircraft engineering (soiling, icing, exterior water management), industrial processes (coating, fire suppression), environmental flows (river and lake hydrodynamics, atmospheric flows), and natural hazards (floods, avalanches, debris flow). Shallow flow models allow capturing the free surface of the fluid with little effort and reducing the three-dimensional problem to a quasi two-dimensional problem through depth-integrating the flow fields. Despite remarkable progress of such models in the last decade, accurate description of complex topography remains a challenge. Interaction with topography is particularly critical for granular flows, because their rheology requires modeling of the pressure field, which is strongly linked to surface curvature and associated centrifugal forces. Shallow granular flow models are usually set up in surface-aligned curvilinear coordinates, and velocity is represented as a two-dimensional surfacealigned vector field. The transformation from Cartesian to curvilinear coordinates introduces fictitious forces, however, which result in complex governing equations. In this paper, we set up the shallow flow model in three-dimensional Cartesian coordinates and preserve three-dimensional velocity in the depthintegrated model. Topography is taken into account with a constraint on velocity. This approach is commonly applied by the thin liquid film community. The advantage is a curvature-free mathematical description that is convenient for complex topographies. The constraint on velocity yields a solution for the pressure field, which is required for the pressure-dependent rheology of granular materials. The model is therefore well-suited for granular flows on three-dimensional terrain, e.g., avalanches. The mathematical model is solved with a second-order accurate, implicit finite area scheme, based on the open source software OpenFOAM. We conduct numerical simulations for various cases to verify the numerical routine based on comparisons with analytical results and a grid refinement study. We establish connections to former solutions and discuss advantages and drawbacks of the proposed method from both mechanical and numerical perspectives.

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Section: Topography Boundary Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A finite area scheme for shallow granular flows on three-dimensional surfaces

Rauter

Tuković

2018

Computers & Fluids

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“…Nevertheless, some of the mass flow models mentioned have been implemented in computational tools used for hazard mapping and zoning, such as DAN (Hungr et al, 1995); TITAN2D (Pitman et al, 2003b;Pitman and Le, 2005); SamosAT (Sampl and Zwinger, 2004); or RAMMS (Christen et al, 2010a, b). Hergarten and Robl (2015) developed a modelling tool relying on the open source flow solver GERRIS (Popinet, 2009).…”

Section: Introductionmentioning

confidence: 99%

r.avaflow v1, an advanced open source computational framework for the propagation and interaction of two-phase mass flows

Mergili¹,

Fischer²,

Krenn³

et al. 2016

Preprint

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Abstract. r.avaflow represents an innovative open source computational tool for routing rapid mass flows, avalanches or process chains from a defined release area down an arbitrary topography to a deposition area. In contrast to most existing computational tools, r.avaflow (i) employs a two-phase, interacting solid and fluid mixture model; (ii) is suitable for modelling more or less complex process chains and interactions; (iii) explicitly considers both entrainment and stopping i.e. the change of the basal topography; (iv) allows for the definition of multiple release masses and/or hydrographs; and (v) serves with built-in functionalities for validation, parameter optimization and sensitivity analysis. r.avaflow is freely available as a raster module of the GRASS GIS software, employing the programming languages Python and C along with the statistical software R. We exemplify the functionalities of r.avaflow by means of two sets of computational experiments: (1) generic process chains consisting in bulk mass and hydrograph release into a reservoir with entrainment of the dam and impact downstream; (2) the prehistoric Acheron rock avalanche, New Zealand. The simulation results are generally plausible for (1) and, after the optimization of two key parameters, reasonably in line with the corresponding observations for (2). However, we identify some potential to enhance the analytic and numerical concepts. Further, thorough parameter studies are necessary in order to make r.avaflow fit for reliable forward simulations of possible future mass flow events.

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“…Physically based dynamic models are used for in-detailed analyses of specific events or situations (e.g., Savage and Hutter, 1989;Takahashi et al, 1992;Iverson, 1997;Pudasaini and Hutter, 2007;Hungr, 2004, 2005;Pitman and Le, 2005;Christen et al, 2010a, b;Mergili et al, 2012b;Pudasaini, 2012;Hergarten and Robl, 2015;. Since the processes are complex in detail and the input parameters are uncertain, simplified conceptual models for the motion of mass flows are today used in combination with GIS (Geographic Information System).…”

Section: Introductionmentioning

confidence: 99%

r.randomwalk v1, a multi-functional conceptual tool for mass movement routing

2015

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Abstract. We introduce r.randomwalk, a flexible and multifunctional open-source tool for backward and forward analyses of mass movement propagation. r.randomwalk builds on GRASS GIS (Geographic Resources Analysis Support System -Geographic Information System), the R software for statistical computing and the programming languages Python and C. Using constrained random walks, mass points are routed from defined release pixels of one to many mass movements through a digital elevation model until a defined break criterion is reached. Compared to existing tools, the major innovative features of r.randomwalk are (i) multiple break criteria can be combined to compute an impact indicator score; (ii) the uncertainties of break criteria can be included by performing multiple parallel computations with randomized parameter sets, resulting in an impact indicator index in the range 0-1; (iii) built-in functions for validation and visualization of the results are provided; (iv) observed landslides can be back analysed to derive the density distribution of the observed angles of reach. This distribution can be employed to compute impact probabilities for each pixel. Further, impact indicator scores and probabilities can be combined with release indicator scores or probabilities, and with exposure indicator scores. We demonstrate the key functionalities of r.randomwalk for (i) a single event, the Acheron rock avalanche in New Zealand; (ii) landslides in a 61.5 km 2 study area in the Kao Ping Watershed, Taiwan; and (iii) lake outburst floods in a 2106 km 2 area in the Gunt Valley, Tajikistan.

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Modelling rapid mass movements using the shallow water equations in Cartesian coordinates

Cited by 31 publications

References 24 publications

A finite area scheme for shallow granular flows on three-dimensional surfaces

A finite area scheme for shallow granular flows on three-dimensional surfaces

r.avaflow v1, an advanced open source computational framework for the propagation and interaction of two-phase mass flows

r.randomwalk v1, a multi-functional conceptual tool for mass movement routing

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