A numerical method for two-phase flows of dense granular mixtures

In this paper, a novel algorithm for incompressible flows of two-phase granular mixtures is proposed. The algorithm constitutes a generalization of projection-type methods to multi-phase flows and employs a predictor-corrector time-marching scheme. For the computation of the phasial pressures, a Poisson equation and a second-order elliptic PDE with variable coefficients are solved at both the prediction and the correction stage. Further, the algorithm is combined with a regularization scheme for the numerical treatment of material interfaces which are a common characteristic of the flows of interest. The efficiency and robustness of the proposed algorithm are illustrated via numerical simulations of unsteady two-dimensional shear flows for a reference mixture of beach sand and water.