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Abstract: In this paper we analyze the equilibrium limit of the constitutive model for two-phase granular mixtures introduced in Papalexandris (2004) , and develop an algorithm for its numerical approximation. At, equilibrium, the constitutive model reduces to a strongly coupled, overdetermined system of quasilinear elliptic partial differential equations with respect to the pressure and the volume fraction of the solid granular phase. First we carry a perturbation analysis based on standard hydrostatic-type scaling arguments which reduces the complexity of the coupling of the equations. The perturbed system is then supplemented by an appropriate compatibility condition which arises from the properties of the gradient operator. Further, based on the Helmholtz decomposition and Ladyzhenskaya’s decomposition theorem, we develop a projection-type, Successive-Over-Relaxation numerical method. This method is general enough and can be applied to a variety of continuum models of complex mixtures and mixtures with micro-structure. We also prove that this method is both stable and consistent hence, under standard assumptions, convergent. The paper concludes with the presentation of representative numerical results. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]