Full three-dimensional simulations of snow-avalanche flow with two-phase, incompressible, granular μ(I) rheology using OpenFOAM / interFoam 

<p align="justify">Protective measures against snow- and landslides are widely used to improve the safety of settlements in avalanche-prone areas. Modelling of granular flow against obstructions is important for the design of catching and deflecting dams and other protective measures in run-out zones and for hazard zoning both below protective measures and in general for avalanche paths with complex terrain geometry. We describe the implementation of a two-phase (granular material and air), incompressible granular-flow rheology for the <em>OpenFOAM / interFoam</em> computational fluid dynamics software system based on the recently developed &#956;(<em>I</em>) granular rheology. The model has been calibrated with observations from eight large Icelandic avalanches and shown to reproduce the observed shapes of the avalanche deposits in the run-out zones, and some available radar measurements of avalanche velocities, with observed and estimated values for avalanche volume and release depth in the starting areas. Several of the avalanches are from paths with complicated geometries, including deep gullies and ridges that split the avalanche in the run-out zone, which indirectly provides <span>constraints</span> on the simulated flow dynamics. The model represents an important improvement with respect to depth-averaged models for snow-avalanche flow in complicated terrain geometries as it is able to simulate the full three-dimensional flow at impact with obstacles such as catching and deflecting dams and braking mounds, including the formation and time-dependent development of hydraulic jumps. Thus, splashing and airborne jets formed at impact with obstacles and landing of granular material on the terrain below obstacles can be modelled, as well as the formation of wedges behind the upstream face of dams or mounds, variations of the flow direction with depth within the flow and thus shearing overflow of the upper part of avalanches at impact with deflecting dams that deflects the main avalanche flow, the effect of the steepness of the upper face of catching and deflecting dams, and the effect of the curvature of the axis of deflecting dams and many other aspects of the flow against obstructions. Some examples of simulations of the flow of design avalanches against protective dams in Iceland will be shown in the presentation.</p>