A well-posed multilayer model for granular avalanches with μ (I) rheology

L. Sarno, Y. C. Tai, Y. Wang, M. Oberlack

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Article number103319
JournalPhysics of Fluids
Issue number10
Publication statusPublished - 2021 Oct 1

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


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