Abstract
The description of geophysical granular flows, like avalanches and debris flows, is a challenging open problem due to the high complexity of the granular dynamics, which is characterized by various momentum exchange mechanisms and is strongly coupled with the solid volume fraction field. In order to capture the rich variability of the granular dynamics along the avalanche depth, we present a well-posed multilayer model, where various layers, made of the same granular material, are advected in a dynamically coupled way. The stress and shear-rate tensors are related to each other by the μ(I) rheology. A variable volume fraction field is introduced through a relaxation argument and is governed by a dilatancy law depending on the inertial number, I. To avoid short-wave instabilities, which are a well-known issue of the conditionally hyperbolic multilayer models and also of three-dimensional models implementing the μ(I) rheology, a physically based viscous regularization using a sensible approximation of the in-plane stress gradients is proposed. Linear stability analyses in the short-wave limit show the suitability of the proposed regularization in ensuring the model well-posedness and also in providing a finite cutoff frequency for the short-wave instabilities, which is beneficial for the practical convergence of numerical simulations. The model is numerically integrated by a time-splitting finite volume scheme with a high-resolution lateralized Harten–Lax–van Leer (LHLL) solver. Numerical tests illustrate the main features and the robust numerical stability of the model.
Highlights
Granular media are ubiquitously involved in industrial applications and natural phenomena, like debris flows and avalanches (e.g., Savage, 1984; Iverson, 1997; Ancey, 2001; Goldhirsch, 2003)
The model incorporates the l(I) rheology (Jop et al, 2005; Jop et al, 2006) and implements a dilatancy law, derived as a generalization of the formula proposed by da Cruz et al (2005)
Assuming that the spatial domain of the avalanche is partitioned into a preset number of layers, the model equations were derived by depthaveraging the mass and momentum balances along each layer and simplified by subsequent long-wave asymptotic approximation, leading to the hydrostatic pressure distribution
Summary
Granular media are ubiquitously involved in industrial applications and natural phenomena, like debris flows and avalanches (e.g., Savage, 1984; Iverson, 1997; Ancey, 2001; Goldhirsch, 2003). While the granular materials are composed of a large number of solid particles, a convenient theoretical approach consists of regarding them as a continuum In this framework, a major open problem concerns an universal rheology capable of describing the broad variety of flow regimes (e.g., Wang and Hutter, 2001; Jop, 2015; Guo et al, 2021). The capability of 3D models of capturing the full dynamics is traded off for a simpler lower-dimensional model While this compromise is acceptable in the case of blunt velocity profiles, typical of avalanches on a smooth bed (e.g., Savage and Hutter, 1989; Gray et al, 1999), it may become inadequate if the velocity profiles are highly sheared or rapidly change in shape (e.g., Silbert et al, 2003; Jop et al, 2005; Lanzoni et al, 2017).
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