Navier-Stokes Equation and Computational Scheme for Non-Newtonian Debris Flow

This paper proposes a computational approach to debris flow model. In recent years, the theoretical activity on the classical Herschel-Bulkley model (1926) has been very intense, but it was in the early 80s that the opportunity to explore the computational model has enabled considerable progress in identifying the subclasses of applicability of different sets of boundary conditions and their approximations. Here we investigate analytically the problem of the simulation of uniform motion for heterogeneous debris flow laterally confined taking into account mainly the geological data and methodological suggestions derived from simulation with cellular automata and grid systems, in order to propose a computational scheme able to operate a compromise between “global” predictive capacities and computing effort. 1. Introduction The mobility of granular clusters in the upper part of the mountain basins may cause a sliding similar to fluids currents. Obviously this happens in particular conditions of slope and if we have a particular solid-fluid concentration ratio. Inside the mixture that moves, there are several resistances. Despite the strong nonstationarity of currents, it is important to study the conditions of uniform or nearly uniform motion [1]. In fact, the phenomenon is so complex as to require the study of the problem in the simplest possible terms. Moreover, the equation of motion obtained in conditions of uniformity is also used in the simulations of variable motion and the uniform motion is an asymptotic condition where the natural currents tend to it in the absence of geometry variations of the contour and of supply conditions. In the case of currents in equilibrium with the bottom it was observed that the velocity profile along the wall has a zero gradient at the bottom. The observations in correspondence with the free surface as well as the first velocity measurements made within the mixture showed that the transverse velocity profile exhibits a maximum at the centerline of the section and minimum values in correspondence with the side walls. Concentration measurements have been obtained by some authors for the case of granular mixtures devoid of fine material, in correspondence with the side walls of the channel. These measurements have shown that the concentration increases with the depth of the current, with a roughly linear trend, reaching a maximum value equal to the concentration at the bottom. In [2] the authors study the motion of a solid-liquid mixture under conditions of uniformity and, above all, they analyze the effect of the walls