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Numerical simulation of 3D free surface flows, with multiple incompressible immiscible phases. Applications to impulse waves
Abstract : A 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 (VOF) 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 finite element method 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, i.e. 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.
https://hal-enpc.archives-ouvertes.fr/hal-01074886
Contributeur : Sébastien Boyaval <>
Soumis le : mercredi 15 octobre 2014 - 17:20:57
Dernière modification le : jeudi 7 février 2019 - 16:21:56
Contributeur : Sébastien Boyaval <>
Soumis le : mercredi 15 octobre 2014 - 17:20:57
Dernière modification le : jeudi 7 février 2019 - 16:21:56