Local penalty methods for flows interacting with moving solids at high Reynolds numbers

An original numerical modelling of multiphase flows interacting with solids in unsteady regimes is presented. Based on the generalized Navier–Stokes equations for multiphase flows and Volume of Fluid (VOF) formulations, an Uzawa minimization algorithm is implemented for the treatment of incompressibility and solid constraints. Augmented Lagrangian terms are added in the momentum equations to speed the convergence of the iterative solver. Defining a priori the penalty parameters which are dedicated to incompressibility and solid constraints is difficult, or impossible, as soon as the flow involves more than one phase and inertia becomes predominant compared to viscous and gravity forces. The Lagrangian penalty terms are calculated automatically according to an original local estimate of the various physical contributions. Numerical validations have been carried out for single particle settling in confined media and viscous flow through a fixed Cubic Faced Centered array. A very good agreement is obtained between experimental, theoretical and numerical results. Extension to unsteady free surface flow interacting with particles is illustrated with the simulation of a dam break flow over moving obstacles.