TRENT2D❄: An accurate numerical approach to the simulation of two-dimensional dense snow avalanches in global coordinate systems

The paper presents a novel and accurate numerical approach to the simulation of two-dimensional, dense snow avalanches described as a single-phase, shallow fluids with a Voellmy friction law. Unlike the majority of the shallow-flow models present in the literature, using a local coordinate system (one axis normal to the bed and the other two lying in the tangent plane), our approach considers a global threedimensional Cartesian coordinate system with an axis opposite to the gravity vector and the other two lying in a horizontal plane. The relevant flow equations, accounting for significant bed slope, have been derived in conservative form for the 1D and 2D cases. This choice allows overcoming an intrinsic limit of the local approach that ceases to be valid in case of vertical walls. From a numerical point of view, the model employs a finite volume scheme applied to a regular Cartesian grid where the fluxes are evaluated with a well-balanced Godunov method. The source term is computed with an implicit operator-splitting technique tailored to deal not only with dynamic conditions but also with stopping conditions due to the Coulomb-type term in the Voellmy friction law. Finally, an effective numerical strategy was developed to treat static conditions with an inclined free surface. Several tests, some with analytical solution and some without, were performed to evaluate the capabilities of the proposed approach. Results are satisfactory: all the analytical solutions are accurately reproduced while the other tests give reliable results. Finally, no instability arises in any situation. For these reasons, TRENT2D❄ is a candidate to become a good model also for practical applications such as hazard mapping and hazard assessments.