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

Nicolas James 1 Alexandre Caboussat 2 Sébastien Boyaval 3, 4 M. Picasso 5
1 LMA-Poitiers - Laboratoire de Mathématiques et Applications
2 Geneva School of Business Administration
3 Saint-Venant - Laboratoire d'Hydraulique Saint-Venant / Saint-Venant Laboratory for Hydraulics
4 MATHERIALS - MATHematics for MatERIALS
ENPC - École des Ponts ParisTech, CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria Paris-Rocquencourt
5 MATHICSE - Mathematics Institute of Computational Science and Engineering [Lausanne]
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.
Keywords : immiscible multiphase flow free surfaces VOF method incompressible liquids density currents impulse waves landslides
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Article dans une revue
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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

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Nicolas James, Alexandre Caboussat, Sébastien Boyaval, M. Picasso. Numerical simulation of 3D free surface flows, with multiple incompressible immiscible phases. Applications to impulse waves . International Journal for Numerical Methods in Fluids, Wiley, 2014, pp.00:1-24. ⟨hal-01074886⟩

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