We re-formulate and demonstrate a new method for particulate flows, the so-called “Smoothed Profile” method (SPM) first proposed in [1]. The method uses a fixed computational mesh, which does not conform to the geometry of the particles. The particles are represented by certain smoothed indicator profiles to construct a smooth body force density term added into the Navier-Stokes equations. The SPM imposes accurately and efficiently the rigid-body constraint inside the particles. In particular, while the original method employs a fully-explicit time-integration scheme, we develop a high-order semi-implicit splitting scheme, which we implement in the context of spectral/hp element discretization. We show that the modeling error of SPM has a non-monotonic dependence on the time step size Δt. The optimum time step size balances the thickness of the Stokes layer and that of the profile interface. Subsequently, we present several numerical simulations, including flow past three-dimensional complex-shaped particles and two interacting microspheres, which are compared against full direct numerical simulations and the force coupling method (FCM).

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