Modeling Hazardous, Free-Surface Geophysical Flows with Depth-Averaged Hyperbolic Systems and Adaptive Numerical Methods

  • D. L. GeorgeEmail author
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 156)


The mathematical modeling and numerical simulation of gravity-driven, free-surface geophysical flows—such as tsunamis, water floods, and debris flows—are described. These shallow flows are often modeled with two-dimensional depth-averaged equations that possess similar mathematical structure: they are usually nonconservative hyperbolic systems with source terms. Some numerical challenges presented by these systems, particularly with regard to features common to depth-averaged models for flow over topography, are highlighted. The open-source software package GeoClaw incorporates numerical algorithms designed to tackle many of the common difficulties presented by depth-averaged models, particularly for large multiscale problems featuring inundation influenced by topography. Some simulation results for tsunamis, floods, and debris flows highlight the capabilities of GeoClaw.


Debris Flow Riemann Problem Shallow Water Equation Riemann Solution Adaptive Mesh Refinement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The work described in this paper has resulted from an active collaboration of researchers in mathematics, computer science, and the geosciences. In particular, Randall LeVeque at the University of Washington, Seattle; Marsha Berger at the Courant Institute, NYU; and Richard Iverson and Roger Denlinger at the U.S. Geological Survey, Vancouver, WA. GeoClaw software development for future applications continues on an active basis, thanks to contributions from Kyle Mandli at the University of Texas, Austin; Dave Yuen at the University of Minnesota; and many others.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.U.S. Geological SurveyVancouverUSA

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