A hyperbolic model for granular flow
Article first published online: 5 AUG 2011
Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Volume 92, Issue 1, pages 72–88, January 2012
How to Cite
Cattani, A., Colombo, R.M. and Guerra, G. (2012), A hyperbolic model for granular flow. Z. angew. Math. Mech., 92: 72–88. doi: 10.1002/zamm.201000181
- Issue published online: 2 DEC 2011
- Article first published online: 5 AUG 2011
- Manuscript Accepted: 20 JUN 2011
- Manuscript Revised: 8 MAR 2011
- Manuscript Received: 12 OCT 2010
- Granular flows;
- non strictly hyperbolic conservation laws.
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.