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In this paper, a segregated algorithm is proposed to suppress high-frequency oscillations in the velocity field for incompressible flows. In this context, a new velocity formula based on a reconstruction of face fluxes is defined eliminating high-frequency errors. In analogy to the Rhie–Chow interpolation, this approach is equivalent to including a flux-based pressure gradient with a velocity diffusion in the momentum equation. In order to guarantee second-order accuracy of the numerical solver, a set of conditions are defined for the reconstruction operator. To arrive at the final formulation, an outlook over the state of the art regarding velocity reconstruction procedures is presented comparing them through an error analysis. A new operator is then obtained by means of a flux difference minimization satisfying the required spatial accuracy. The accuracy of the new algorithm is analyzed by performing mesh convergence studies for unsteady Navier–Stokes problems with analytical solutions. The stabilization properties of the solver are then tested in a problem where spurious numerical oscillations arise for the velocity field. The results show a remarkable performance of the proposed technique eliminating high-frequency errors without losing accuracy. [ABSTRACT FROM AUTHOR]

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]