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Quadrature-based moment methods for multiphase flows

Several complex flows can be conveniently described at a mesoscopic level, where a probability density function (PDF) is used as a compromise between full a Lagrangian description and averaged (i.e., mean field) Eulerian formulations. Well known examples of this approach are the population balance equation (aka Smoluchowski coagulation equation), the Generalised Boltzmann equation, and PDF methods for turbulent flows. In this talk we will focus on the problem of polydispersed particulate processes in turbulent flows and in porous materials. We will present a family of numerical methods for the solution of this kind of PDF equations, namely the Quadrature-based moment methods (QBMM), based on the classical method of moments, with closures based on Gaussian quadrature rules. First introduced by McGraw in 1997 for aerosols, these have been developed and extended to deal with many interesting problems in fluid dynamics and, in general, in applied mathematics. Applications to large eddy simulation of particle-laden flows and to the upscaling of DNS simulations in porous materials will be considered.