Time-Splitting Procedure for the Resolution of the Volume Fraction for Unsteady Flows

摘要

Numerical simulations of multifluid flows using interface capturing schemes are highly constrained by the Courant-Friedrichs-Lewy (CFL) condition. Even with implicit codes, the Courant number Co is limited to values lower than unity in order to benefit from compressive properties of the schemes and to restrict the diffusion of the interface [6, 9]. Therefore the usable time steps become rapidly redhibitory since they are linked to the grid by the definition of Co and since, if the grid is refined, the time step must be reduced accordingly. This is particularly true when the free surface undergoes large and violent deformations, as in the case of a rowing stroke in water [3, 8] or a prism impacting a free surface [2, 10]. The equation subject to this condition is the convection equation of the volume fraction of water c.