Modeling rapid mass movements using the shallow water equations
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We propose a new method to
model rapid mass movements on complex topography using the shallow water
equations in Cartesian coordinates. These equations are the widely used standard
approximation for the flow of water in rivers and shallow lakes, but the main
prerequisite for their application – an almost horizontal fluid table – is in
general not satisfied for avalanches and debris flows in steep terrain.
Therefore, we have developed appropriate correction terms for large topographic
gradients. In this study we present the mathematical formulation of these
correction terms and their implementation in the open-source flow solver GERRIS.
This novel approach is evaluated by simulating avalanches on synthetic and
finally natural topographies and the widely used Voellmy flow resistance law.
Testing the results against analytical solutions and the proprietary avalanche
model RAMMS, we found a very good agreement. As the GERRIS flow solver is freely
available and open source, it can be easily extended by additional fluid models
or source areas, making this model suitable for simulating several types of
rapid mass movements. It therefore provides a valuable tool for assisting
regional-scale natural hazard studies.