Numerical simulation of snow avalanches as a Bingham fluid flow using SPH method

In this paper, a Lagrangian formulation of the Navier-Stokes equations, based on the Smoothed Particle Hydrodynamics (SPH) method, was applied to simulate snow avalanches as a Bingham fluid. In order to simulate snow avalanches, the constitutive equation of a Bingham fluid was implemented into the SPH model. The Bingham constitutive model is formulated based on coulomb's failure criterion, in which the cohesion and friction angle are the only parameters required to estimate the material viscosity. An equivalent Newtonian viscosity is calculated to express the Bingham viscosity into Navier-Stokes equations. The model was performed to simulate the collapse of water-clay mix column. Results showed that SPH method is able to simulate non-Newtonian fluid. A simple snow avalanche experiment was simulated and the computational results showed good agreement with the experimental results and the model is considered a good tool to simulate snow avalanche phenomena.