Mathematical Modeling of Powder‐Snow Avalanche Flows

Abstract

Abstract. Powder-snow avalanches are violent natural disasters which represent a major risk for infrastructures and populations in mountain regions. In this study we present a novel model for the simulation of avalanches in the aerosol regime. The second scope of this study is to get more insight into the interaction process between an avalanche and a rigid obstacle. An incompressible model of two miscible fluids can be successfully employed in this type of problems. We allow for mass diffusion between two phases according to the Fick's law. The governing equations are discretized with a contemporary fully implicit finite volume scheme. The solver is able to deal with arbitrary density ratios. Several numerical results are presented. Volume fraction, velocity and pressure fields are presented and discussed. Finally we point out how this methodology can be used for practical problems.

Simulations of non homogeneous viscous flows with incompressibility constraints

“…-We obtain very similar results (up to a slight change of units which need to be corrected in [26]).…”

“…• Assume an ad hoc relation between µ and κ: with µ = µ 0 +μρ and κ =μ, the higher order terms cancel out and, furthermore a remarkable energy identity can be established, as observed in [26,11,21,52].…”

“…Another set of simulations appeared in [27,28], based on a version of the KS system, with a Finite Element scheme coupled to characteristic methods for the convection terms; the simulations also use mesh refinements strategies in order to follow the advance of the front. Finally [26] uses OpenFoam, on a fixed Cartesian mesh to produce numerical avalanches by using the KS system.…”

“…Let us end this introduction with a few words about potential applications of our approaches. Powder-snow avalanches is a relevant example of the kind of fluid mixtures we are considering and variations about the Navier-Stokes system have been used successfully to reproduce certain features of laboratory avalanches [26,27,28]. These complex models also naturally arise in combustion theory; nuclear safety engineering provides further relevant examples of applications, see for instance the works [24,6,59] motivated by security computations for PWR reactors.…”

An Improved Mathematical Model for Geological Analysis of Debris Flow

“…The other approach is based on the full Navier-Stokes equations (incompressible flow), the interface tracking method will be used to describe the interface distribution and motion characteristics. Different numerical models are conducted to simulate the dam-break problem (Biscarini et al, 2010), landslide runout (Vassilevski et al, 2012), landslide generated water waves (Biscarini, 2010) and snow avalanche impacting barriers (Dutykh et al, 2011). The second approach is similar to the shallow water equation, which is widely used to simulate the dam break and flood disasters and many achievements have been obtained in the numerical simulations and experiments (Xu et al, 2012;Maleewong, 2011).…”