Numerical simulation of 3D free surface flows, with multiple incompressible immiscible phases. Applications to impulse waves

• Published in: International journal for numerical methods in fluids 2014-12, Vol.76 (12), p.1004-1024
• Main Authors: James, N., Boyaval, S., Caboussat, A., Picasso, M.
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Fluid flow; free surfaces; immiscible multiphase flow; impulse waves; Impulses; Incompressible flow; incompressible liquids; landslides; Liquid phases; Mathematical models; Navier-Stokes equations; Phases; VOF method
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.3967

SUMMARYA numerical method for the solution to the density‐dependent incompressible Navier–Stokes equations modeling the flow of N immiscible incompressible liquid phases with a free surface is proposed. It allows to model the flow of an arbitrary number of liquid phases together with an additional vacuum phase separated with a free surface. It is based on a volume‐of‐fluid approach involving N indicator functions (one per phase, identified by its density) that guarantees mass conservation within each phase. An additional indicator function for the whole liquid domain allows to treat boundary conditions at the interface between the liquid domain and a vacuum. The system of partial differential equations is solved by implicit operator splitting at each time step: first, transport equations are solved by a forward characteristics method on a fine Cartesian grid to predict the new location of each liquid phase; second, a generalized Stokes problem with a density‐dependent viscosity is solved with a FEM on a coarser mesh of the liquid domain. A novel algorithm ensuring the maximum principle and limiting the numerical diffusion for the transport of the N phases is validated on benchmark flows. Then, we focus on a novel application and compare the numerical and physical simulations of impulse waves, that is, waves generated at the free surface of a water basin initially at rest after the impact of a denser phase. A particularly useful application in hydraulic engineering is to predict the effects of a landslide‐generated impulse wave in a reservoir. Copyright © 2014 John Wiley & Sons, Ltd. A numerical method for the simulation of multiphase flows involving several incompressible immiscible liquid phases and a free surface is presented. A volume‐of‐fluid approach is used to track the multiple phases, whereas an operator splitting algorithm and a two‐grid method allow the decoupling of transport and diffusion phenomena. This new algorithm is applied in particular to hydraulic engineering for the simulation of landslide‐generated impulse waves generated at the free surface of a water reservoir.