Upwinded finite difference schemes for dense snow avalanche modeling

Avalanche dynamics models are used by engineers and land-use planners to predict the reach and destructive force of snow avalanches. These models compute the motion of the flowing granular core of dense snow avalanches from initiation to runout. The governing differential equations for the flow height and velocity can be approximated by a hyperbolic system of equations of first-order with respect to time, formally equivalent to the Euler equations of a one-dimensional isentropic gas. In avalanche practice these equations are presently solved analytically by making restrictive assumptions regarding mountain topography and avalanche flow behaviour. In this article the one-dimensional dense snow avalanche equations are numerically solved using the conservative variables and stable upwinded and total variation diminishing finite difference schemes. The numerical model is applied to simulate avalanche motion in general terrain. The proposed discretization schemes do not use artificial damping, an important requirement for the application of numerical models in practice. In addition, non-physical M-wave solutions are not encountered as in previous attempts to solve this problem using Eulerian finite difference methods and non-conservative variables. The simulation of both laboratory experiments and a field case study are presented to demonstrate the newly developed discretization schemes.