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Advanced Numerical Modeling of Debris Flows and Rock Avalanches: David George
Project Title: Advanced Numerical Modeling of Debris Flows and Rock Avalanches
Mendenhall Fellow: David George,, (360) 993-8932
Duty Station: Cascades Volcano Observatory, Vancouver, WA
Start Date: October 1, 2008
Education: Ph.D., Applied Mathematics, University of Washington, Seattle, 2006
Research Advisors: Richard Iverson, (360) 993-8920,; Roger Denlinger, (360) 993-8904,; Mark Reid, (650) 329-4891,

Project Description: A large class of hazardous geophysical flows, such as landslides, avalanches and other debris flows, are characterized by a relatively shallow gravity-driven free-surface flow. Because of the complex, heterogeneous and dynamic rheology of these flows, it is not possible to reduce the governing equations to traditional equations in continuum mechanics or fluid dynamics. Therefore, despite the prevalence of these hazards, mathematical models for such flows are relatively recent and largely untested. Additionally, specialized numerical methods for solving such equations have not been thoroughly developed. While three-dimensional models provide useful theoretical insight into the physics and rheology of an idealized flow, they are computationally intractable for simulating large-scale real-world events. An alternative approach is to used depth-averaged equations where the vertical variation in the flow has been integrated, reducing the problem to two dimensions. Such a model has been developed for debris
flows by U.S. Geological Survey (USGS) scientists Richard Iverson and Roger Denlinger (Denlinger and Iverson, 2004; Iverson and others, 2004) and compared to controlled landslide experiments, both laboratory scale and at the large-scale USGS
flume facility in central Oregon. Iverson and Denlinger's mathematical model appears promising and continues to be refined as the physics of debris flows is elucidated through these experiments. However, the mathematical model presents challenges for numerical solution, prompting the development of new numerical methods and software to make even this two-dimensional system computationally tractable
for real-world hazard simulations.

The goal of this project is to extend the numerical methods and software developed by George and LeVeque (2006) for solving (depth-averaged) shallow water equations in the context of tsunami simulation to Iverson and Denlinger's model for debris flows. A key component of this software is the use of adaptive mesh refinement (AMR) to track important dynamic features in the solution, refining those features on fine-scale moving grids, while steady states are preserved on much coarser grids. Adaptive mesh refinement makes these problems computationally feasible. For instance, with AMR it is possible to model transoceanic tsunami propagation as well as local coastal inundation in single global-scale simulations, by having grids of various refinements track the waves and refine further as the waves inundate impacted coastlines. For debris flows, where the localized flowing mass moves rapidly and unpredictably throughout a much larger domain, AMR allows the flowing mass to be resolved on highly refined moving grids that would be too expensive to use over the whole domain. While many numerical challenges still remain to be solved before these methods can be accurately and robustly applied to Iverson and Denlinger's debris flow model, one eventual goal of this project is to create a freely available software package for scientists at the USGS and elsewhere to use for studying potentially hazardous surface

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Figure 1. A, Figure of a numerical simulation of a debris flow using Denlinger and Iverson's single grid code. B, Simulation of the 2004 Indian Ocean tsunami using GeoClaw, George and LeVeques code. Three levels are shown; a coarse level remains to the left away from waves, finer grids surround the waves for deep ocean propagation, and the finest grids appear as waves inundate Sri Lanka (grid lines omitted from finest grids). Actual simulation included the entire Indian Ocean, and runs in less than an hour on a single processor laptop (see, for example, George and LeVeque, 2006).

Denlinger, R.P., and Iverson, R.M., 2004, Granular avalanches across irregular three-dimensional terrain, 1, Theory and computation: Journal of Geophysical Research, v. 109, F01014.

George, D.L., and LeVeque. R.J., 2006, Finite volume methods and adaptive refinement for global tsunami propagation and inundation: Science of Tsunami Hazards, v. 24, no. 5, p. 319–328.

Iverson, R.M., Logan, M., and Denlinger, R.P., 2004, Granular avalanches across irregular three-dimensional terrain, 2, Experimental tests: Journal of Geophysical Research, v. 109, F01015.

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Last modified: 16:08:28 Thu 13 Dec 2012