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In this paper, we present a high fidelity conservative and adaptive level-set method for the simulation of two-fluid flows. A new level-set method is designed that associates both re-initialization and convection steps in an implicit manner. Thus the new obtained convection-reaction problem is solved using a stabilized finite element method. The accuracy, the time scheme and the mass conservation are thoroughly analyzed. Anisotropic meshing with conservative interpolation is implemented and tested on several benchmarks including splashes, sloshing and complex bubble dynamics.

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International audiencePurpose - This paper aims to develop a robust set of advanced numerical tools to simulate multiphase flows under the superimposition of external uniform magnetic fields. Design/methodology/approach - The flow has been simulated in a fully Eulerian framework by a {\it variational multi-scale} method, which allows to take into account the small-scale turbulence without explicitly model it. The multi-fluid problem has been solved through the convectively re-initialized level-set method to robustly deal with high density and viscosity ratio between the phases and the surface tension has been modelled implicitly in the level-set framework. The interaction with the magnetic field has been modelled through the classic induction equation for 2D problems and the time step computation is based on the electromagnetic interaction to guarantee convergence of the method. Anisotropic mesh adaptation is then used to adapt the mesh to the main problem's variables and to reach good accuracy with a small number of degrees of freedom. Finally, the variational multiscale method leads to a natural stabilization of the finite elements algorithm, preventing numerical spurious oscillations in the solution of Navier-Stokes equations (fluidmechanics) and the transport equation (level-set convection). Findings - The methodology has been validated, and it is shown to produce accurate results also with a low number of degrees of freedom. The physical effect of the external magnetic field on the multiphase flow has been analysed. Originality/value - The dam-break benchmark case has been extended to include magnetically constrained flow

International audienceAerodynamic characteristics of various geometries are predicted using a finite element formulation coupled with several numerical techniques to ensure stability and accuracy of the method. First, an edge based error estimator and anisotropic mesh adaptation are used to detect automatically all flow features under the constraint of a fixed number of elements, thus controlling the computational cost. A Variational MultiScale stabilized finite element method is employed to solve the incompressible Navier-Stokes equations. Finally, the Spalart-Allmaras turbulence model is solved using the Streamline Upwind Petrov-Galerkin (SUPG) method. This paper is meant to show that the combination of anisotropic unsteady mesh adaptation with stabilized finite element methods provides an adequate framework for solving turbulent flows at high Reynolds numbers. The proposed method was validated on several test cases by confrontation with literature of both numerical and experimental results, in terms of accuracy on the prediction of the drag and lift coefficients as well as their evolution in time for unsteady cases. This article is protected by copyright. All rights reserved

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