  A numerical model and parallel software for 3D simulations of granular flows
have been developed based on the Lagrangian particle (LP) method [R.Samulyak,
X. Wang, H.-C. Chen, Lagrangian particle method for compressible fluid
dynamics, J. Comput. Phys. 362 (2018) 1-19], originally developed for
compressible hydrodynamic flows, including free surface / multiphase problems.
LP uses local polynomial least square fittings on particle-based stencils that
ensure numerical convergence to the prescribed order. The granular flow model
implements continuum equations with a $\mu(I)$-rheology closure that is capable
of describing two-directional transitions of the flow between various regimes
characterized by solid-, liquid-, and gas-like features. The granular flow code
has been parallelized for distributed memory supercomputers and validated by
comparing 3D simulations to experimental data on the collapse of granular
columns. Numerical simulations showing the granular flow transition to a
gas-like regime have also been presented.
