A numerical approach for simulating two-dimensional dense-snow avalanches in global coordinate systems

<p>Snow avalanche models are commonly based on a continuum fluid scheme, on the assumption of shallow flow in the direction normal to the bed, on a depth-averaged description of the flow quantities and on different assumptions concerning the velocity profile, the friction law, and the pressure in the flow direction (see Bartelt et al, 1999, Barbolini et al., 2000, for an overview). The coordinate reference system is commonly local, i.e., for each point of the domain, one axis is normal to the bed while the other two axes lay in a tangent plane. When the bed is vertical and the flow is not aligned with the steepest direction (e.g., in case of a side wall), the flow depth is no longer defined considering the normal direction and the model based on the local coordinate system is no longer valid. In near-vertical conditions, numerical problems can be expected.</p><p>Another critical point, for numerical models based on finite volume schemes and Godunov fluxes, is the accurate treatment of the source term in case of no-motion conditions (persistence, starting and stopping of the flow) due to the presence of velocity-independent, Coulomb-type terms in the bed shear stress. </p><p>In this work, we provide a numerical approach for a Voellmy-fluid based model, able to overcome the limits depicted above, to accurately simulate analytical solutions and to give reliable solutions in other cases (Zugliani & Rosatti, 2021). Firstly, differently from the other literature models, the chosen coordinate reference system is global (an axis opposite the gravity vector and the other two orthogonal axes lay in the horizontal plane) and therefore, the relevant mass and momentum equations have been derived accordingly. Secondly, these equations have been discretized by using a finite volume method on a Cartesian square grid where the Godunov fluxes has been evaluated by mean of a modified DOT scheme (Zugliani & Rosatti, 2016) while source terms in conditions of motion have been discretized by using an implicit operator-splitting technique. Finally, a specific algorithm has been derived to deal with the source term to determine the no-motion conditions.  Several test cases assess the capabilities of the proposed approach.</p><p> </p><p><strong>References:</strong></p><p>Barbolini, M., Gruber, U., Keylock, C.J., Naaim, M., Savi, F. (2000), <em>Application of statistical and hydraulic-continuum dense-snow avalanche models to five real European sites.</em> Cold Regions Science and Tech. 31, 133–149.</p><p>Bartelt, P., Salm, B., Gruber, U. (1999), <em>Calculating dense-snow avalanche runout using a voellmy-fluid model with active/passive longitudinal straining.</em> Journal of Glaciology 45, 242-254.</p><p>Zugliani D., Rosatti G. (2021), <em>Accurate modeling of two-dimensional dense snow avalanches in global coordinate system: the TRENT2D<sup>❄</sup> approach. </em>Paper under review.</p><p>Zugliani, D., Rosatti, G. (2016), <em>A new Osher Riemann solver for shallow water flow over fixed or mobile bed</em>, Proceedings of the 4th European Congress of the IAHR, pp. 707–713.</p>

AvaFrame as a testing and benchmarking environment for avalanche simulations

<p>Testing and benchmarking avalanche models is a crucial step in developing models as well as assessing their applicability. This is not only limited to the representation of physical processes within models, be it via first principles or using empirical relationships, but also concerns their computing environment, including compilers, hardware used, programming language, among others. </p><p>Test, benchmarking, and comparison strategies can aim at different issues, among others: numerics, the implementation thereof, plausibility, verification, or evaluation. However, they always require reference or expected results. References can come from observations, analytical results, comparison to other models, known physical processes or material properties that cannot be changed – e.g., “avalanches cannot fly”. The question is: which characteristics or properties do we test and how to design appropriate tests?  </p><p>To facilitate this, as part of the newly developed opensource avalanche framework - AvaFrame -, we started providing commonly accessible tools to make testing and developing easier. This ranges from tools to import data, generate input parameters to automatic analysis and plotting. Not only do we provide the infrastructure for testing, but we also provide a set of test cases complete with all necessary input data, reference results, and run script examples. These tests so far include idealized (generic) topographies, specific test cases for numerical questions, and 6 real world avalanches with distinct characteristics. </p><p>In this contribution we present this freely available set of tests and benchmarks suitable to assess various aspects and properties of a shallow water model solver for a dense flow avalanche model, one of the core computing modules of AvaFrame (com1DFA). We highlight how we utilize the entire range of tests in our continuous model development to assure the quality and applicability / validity of our development. Showing results from comparison to existing models, but also how to extend and apply our strategies to other models or research questions, we invite other researchers and developers to make full use of these tools.</p>

Water Waves Provide Insight Into Landslides and Avalanche Models

Boussinesq-type gravity waves appear to accurately describe vertical motion in granular flows found in geophysics.