We present a model that describes the motion of some granular material sliding along a slope. During this movement, both erosion and deposition may take place, depending on the speed of the sliding material. Analytically, this model consists of a hyperbolic system of partial differential equations. In the 1D case, the resulting system of balance laws displays interesting behavior. Its convective part gives rise to a 3 × 3 globally well defined Riemann Problem, in spite of the appearance of vacuum and of the lack of strict hyperbolicity. Several numerical integrations show various features of this model.
Cattani, A., Colombo, M., Guerra, G. (2012). A hyperbolic model for granular flow. ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND MECHANIK, 92(1 (January 2012)), 72-88 [10.1002/zamm.201000181].
A hyperbolic model for granular flow
GUERRA, GRAZIANO
2012
Abstract
We present a model that describes the motion of some granular material sliding along a slope. During this movement, both erosion and deposition may take place, depending on the speed of the sliding material. Analytically, this model consists of a hyperbolic system of partial differential equations. In the 1D case, the resulting system of balance laws displays interesting behavior. Its convective part gives rise to a 3 × 3 globally well defined Riemann Problem, in spite of the appearance of vacuum and of the lack of strict hyperbolicity. Several numerical integrations show various features of this model.
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