The two-layer shallow water system looses hyperbolicity if the mag- nitude of the shear velocity is above a certain threshold, which is es- sentially determined by the density difference between the two layers. The focus of the paper is to explore a technique to possibly recover hyperbolicity by adapting the model in regions of strong shear. The approach is to introduce an additional, third layer in such regions. We demonstrate that this adaptive two/three-layer approach can cure some of the shortcomings of the two-layer model but needs further improvement with respect to the model.
On the hyperbolicity of two and three layer shallow water equations
PUPPO, GABRIELLA ANNA
2012-01-01
Abstract
The two-layer shallow water system looses hyperbolicity if the mag- nitude of the shear velocity is above a certain threshold, which is es- sentially determined by the density difference between the two layers. The focus of the paper is to explore a technique to possibly recover hyperbolicity by adapting the model in regions of strong shear. The approach is to introduce an additional, third layer in such regions. We demonstrate that this adaptive two/three-layer approach can cure some of the shortcomings of the two-layer model but needs further improvement with respect to the model.
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