A finite area scheme for shallow granular flows on threedimensional surfaces
Abstract
Shallow flow or thin liquid film models are used for a wide range of physical and engineering problems. Shallow flow models allow capturing the free surface of the fluid with little effort and reducing the threedimensional problem to a quasi twodimensional problem through depthintegrating the flow fields. Despite remarkable progress of such models in the last decade, accurate description of complex topography remains a challenge. Interaction with topography is particularly critical for granular flows, because their rheology requires modeling of the pressure field, which is strongly linked to surface curvature and associated centrifugal forces. Shallow granular flow models are usually set up in surfacealigned curvilinear coordinates, and velocity is represented as a twodimensional surfacealigned vector field. The transformation from Cartesian to curvilinear coordinates introduces fictitious forces, however, which result in complex governing equations. In this paper, we set up the shallow flow model in threedimensional Cartesian coordinates and preserve threedimensional velocity in the depthintegrated model. Topography is taken into account with a constraint on velocity. This approach is commonly applied by the thin liquid film community. The advantage is a curvaturefree mathematical description that is convenient for complex topographies. The constraint on velocity yields a solution for the pressure field, which is required for the pressuredependent rheology of granular materials. The model is therefore wellsuited for granular flows on threedimensional terrain, e.g., avalanches.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1802.05229
 Bibcode:
 2018arXiv180205229R
 Keywords:

 Physics  Computational Physics
 EPrint:
 accepted