Smoothed profile method for particulate flows: Error analysis and simulations

We re-formulate and analyze a new method for particulate flows, the so-called “smoothed profile” method (SPM) first proposed in [Y. Nakayama, R. Yamamoto, Simulation method to resolve hydrodynamic interactions in colloidal dispersions, Phys. Rev. E 71 (2005) 036707], which uses a fixed computational mesh without conformation to the geometry of the particles. The method represents the particles by certain smoothed profiles to construct a body force term added into the Navier–Stokes equations. SPM imposes accurately and efficiently the proper conditions at the particle–fluid interface. 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. First, we show that the modeling error of SPM has a non-monotonic dependence on the time step size Δ t ; it is a function of ν Δ t / ξ , where ν is the kinematic viscosity of fluid and ξ is the interface thickness of the smoothed profile. Subsequently, we present several steady and unsteady simulations, including flow past 3D complex-shaped particles, and compare against direct numerical simulations and the force coupling method (FCM).