Augmented Lagrangian and penalty methods for the simulation of two-phase flows interacting with moving solids. Application to hydroplaning flows interacting with real tire tread patterns

The numerical simulation of the interaction between a free surface flow and a moving obstacle is considered for the analysis of hydroplaning flows. A new augmented Lagrangian method, coupled to fictitious domains and penalty methods, is proposed for the simulation of multiphase flows. The augmented Lagrangian parameter is estimated by an automatic analysis of the discretization matrix resulting from the approximation of the momentum equations. The algebraic automatic augmented Lagrangian 3AL approach is validated on the natural convection in a differentially heated cavity, a two-dimensional collapse of a water column, the three-dimensional settling of a particle in a tank and the falling of a dense cylinder in air. Finally, the 3AL method is utilized to simulate the hydroplaning of a tire under various pattern shape conditions. key-words fictitious domain, augmented Lagrangian, 1-fluid model, penalty method, Volume Of Fluid, 1 patterned tire, hydroplaning flows