This study investigates a fictitious domain model for the numerical solution of various incompressible viscous flows. It is based on the so‐called Navier–Stokes/Brinkman and energy equations with discontinuous coefficients all over an auxiliary embedding domain. The solid obstacles or walls are taken into account by a penalty technique. Some volumic control terms are directly introduced in the governing equations in order to prescribe immersed boundary conditions. The implicit numerical scheme, which uses an upwind finite volume method on staggered Cartesian grids, is of second‐order accuracy in time and space. A multigrid local mesh refinement is also implemented, using the multi‐level Zoom Flux Interface Correction (FIC) method, in order to increase the precision where it is needed in the domain. At each time step, some iterations of the augmented Lagrangian method combined with a preconditioned Krylov algorithm allow the divergence‐free velocity and pressure fields be solved for. The tested cases concern external steady or unsteady flows around a circular cylinder, heated or not, and the channel flow behind a backward‐facing step. The numerical results are shown in good agreement with other published numerical or experimental data. Copyright © 2000 John Wiley & Sons, Ltd.

International audienceThe scope of this work is to present and discuss the results obtained from simulating three-dimensional plunging breaking waves by solving the Navier-Stokes equations, in air and water, coupled with a dynamic subgrid scale turbulence model (Large Eddy Simulation, LES). An original numerical tool is used for the complete description of the plunging breaking processes including overturning, splash-up and the occurrence of air entrainment. The first part of the paper is devoted to the presentation and the validation of the numerical models and methods. Initial 3D conditions corresponding to unstable periodic sinusoidal waves of large amplitudes in periodic domains are then used to study further the ability of the numerical model to describe accurately the air entrainment occurring when waves break. The numerical results highlight the major role of this phenomenon in the energy dissipation process, through a high level of turbulence generation. The numerical model represents a substantial improvement in the numerical modelling of breaking waves since it includes the air entrainment process neglected in most previous existing models

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