Continuum modelling of snow avalanches using an adaptive-mesh open-source finite element framework (MS)

Abstract

A snow avalanche is a natural free-surface flow phenomenon that occurs in mountainous regions frequently. The mountainous areas of the Himalayas and the Alps have witnessed many casualties, including the collapse of buildings, roads, and highways. While designing appropriate preventive measures, bridges, and defense structures, a detailed analysis is crucial. The continuum conceptualisation of the flow results in mass and momentum partial differential equations, which can be solved to obtain the flow fields such as pressure, velocity and fluid interface. A constitutive (or rheological) model is required to "close" the above set of governing equations. Many past experiments reveal that flowing snow behaves similar to non-Newtonian fluids. The resultant coupled equations are non-linear partial differential equations, which require a numerical method to solve them. The present work deals with the continuum modelling of snow avalanches, emphasising the non-Newtonian fluid dynamics. An implementation of non-Newtonian models was carried out in an open-source finite element method (FEM) based computational fluid dynamics (CFD) code. FEM provides added advantages of dealing with complex geometries using unstructured, anisotropic meshes. The accuracy of the solution increases by changing the order of polynomial in the basis functions in the discretisation. The credibility of the new implementation was ensured at each step through rigorous verification, benchmarking, and validation. A channel flow problem was first solved with the power-law rheological model, and the results were verified with the existing analytical solutions. Different discretisation schemes were tested for the velocity-pressure element pair to demonstrate the order of convergence. Benchmarking was then performed for a 2-D lid-driven cavity problem (using the power-law fluid model) against the lattice Boltzmann method (LBM). A 2-D dam-break problem with the Carreau-Yasuda (CY) rheological model was then simulated and validated with an experiment. Another validation was carried out by simulating a snow-chute problem using the Cross rheological model, followed by a real snow avalanche simulation on actual mountain topography. Since the existing CFD solvers are compute intensive while dealing with three-dimensional domains, the novelty of the current work lies in modelling snow avalanche dynamics on real mountain topography using parallel, unstructured, anisotropic mesh adaptivity. The current framework can be extended to solve industrial problems like the flow of materials in process industries, pharmaceuticals, and mining.